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Playing With Numbers Class 6 Notes CBSE Maths Chapter 3 (Free PDF Download)

• Revision Notes
• Chapter 3 Playing With Numbers

Exam - Focused Revision Notes for CBSE Class 7 Maths Chapter 2 - Fractions and Decimals

Unlock the power of seamless learning with Vedantu's exclusive offering: a free downloadable PDF format for CBSE Class 6 Maths Chapter 3 - Playing With Numbers. Our user-friendly webpage provides easy access to this comprehensive resource, designed to enhance your understanding of number theory. Delve into the exciting world of mathematical concepts with step-by-step solutions, elucidating complex topics in a simple and engaging manner. Empower yourself with the convenience of studying anytime, anywhere, and at your own pace. Let Vedantu be your trusted companion on your academic journey, as we strive to make learning an enjoyable and rewarding experience for every student.

Also download the free PDF format for a hassle-free learning experience. At Vedantu.com, we go beyond just offering study materials; students can also enroll for interactive online NCERT Class 6 Science tuition to ace their CBSE board exams. Our platform is dedicated to providing comprehensive support to learners, including free CBSE Solutions (NCERT) and other valuable resources. For math enthusiasts seeking superior solutions, Class 6 Maths NCERT Solutions are readily available to help you master the syllabus and achieve higher scores in your examinations.

Access Class 6 Mathematics Chapter 3 – Playing with Numbers Notes in 30 Minutes

Factors And Multiples

If a number $n$ is the exact divisor of the number $m$ then $n$ is the factor of $m$ i.eThe factor of a number is the exact divisor of that number.

A number always has at least two factors i.e., $1$ and the number itself.

Every factor is less than or equal to the given number and is finite.

For example: Factors of $20$ are $2,10,5$ and $4$ 

A perfect number is whose sum of all the factors is equal to twice the number.

Multiple is the product of two or more numbers

A number always have at least one multiple i.e., the number itself

Multiples is always greater than or equal to the given number and multiples of a number is infinite.

For example: $5\times 4=20$ here $20$ is the multiple of $5$ and $4$

Prime And Composite Numbers

Prime numbers are the numbers which are divisible only by $1$ and the number itself i.e., a prime number always have only two factors.

$2$ is the only prime number which is even and all other prime numbers are odd.

For example: $2,3,5,7,11,13,17$ etc. are the prime numbers

Composite numbers are the numbers which are divisible by more than two factors i.e., composite number have more than two factors.

For example: $4,6,8,10,12,14,$ etc.

$1$ has only one factor i.e., $1$ itself so it is neither prime nor composite number.

Even numbers are those number which are the multiples of $2$ 

Odd numbers are those number which are not the multiples of $2$

Test for Divisibility of Numbers

1. Divisibility by $10$ 

A number is divisible by $10$ when its ones digit is $0$ then only it is the multiple of $10$ 

For example: $520,950,630,20$ etc.

2. Divisibility by $5$

A number is divisible by $5$ when its ones digit is either $0$ or $5$ then only it is the multiple of $5$ 

For example: $50,95,65,20$ etc.

3. Divisibility by $2$ 

A number is divisible by $2$ when its one’s digit is $0,2,4,6$ or $8$ i.e., every even number is divisible by $2$ 

For example: $50,92,64,26,68$ etc.

4. Divisibility by $3$  

A number is divisible by $3$ when sum of its digit is divisible by $3$ 

For example: $7263$, the sum of digits of $7263$ is $18$ and $18$ is divisible by $3$ therefore $7263$ is also divisible by $3$

5. Divisibility by $6$ 

A number is divisible by $6$ only if it is divisible by $2$ and $3$ both.

For example: $6,12,18,24,36$ etc.

6. Divisibility by $4$ 

One digit and two-digit number divisibility by $4$ is checked by actual division.

But three or more-digit number is divisible by $4$ if the number formed by the last two digit is divisible by $4$ 

For example: $1000,3012,523612$ etc.

7. Divisibility by $8$ 

One digit to three-digit number divisibility by $8$ is checked by actual division.

But four or more-digit number is divisible by $8$ if the number formed by the last three digit is divisible by $8$ 

8. Divisibility by $9$

A number is divisible by $9$ when sum of its digit is divisible by $9$ 

For example: $215847$,  the sum of digits of $215847$ is $27$ and $27$ is divisible by $9$ therefore $215847$ is also divisible by $9$

9. Divisibility by $11$ 

If the difference between the sum of the digits at odd places and the sum of the digits at even places of the number is either $0$ or divisible by $11$, then the number is divisible by $11$ 

For example:

$61809$ 

Sum of digits at odd places$=6+8+9=23$ 

Sum of digits at even places$=1+0=1$ 

Now, difference between the sum of the digits at odd places and the sum of the digits at even places$=23-1=22$ 

Since, $22$ is divisible by $11$ 

Therefore, $61809$ is also divisible by $11$

Common Factor Or Common Multiple

A factor which is common in two or more numbers is called common factor.

For example:  

Factors of $8$ are $1,2,4$ and $8$ 

Factors of $12$ are $1,2,3,4,6$and $12$ 

$\therefore 4$ is the common factor of $8$ and $12$ 

A multiple which is common to two or more numbers is called common multiple.

Multiple of $2$ are $4,6,8,10,12$ and $18$ 

Multiple of $3$ are $6,9,12,15,18$ and $21$ 

$\therefore 6,12$ and $18$ are common multiple of $2$ and $3$ 

Co-prime are those number which have $1$ as common factors.

For example: $5,8,69,52,41$ etc. are co-primes

Some More Divisibility Rules

If a number is divisible by another number, then it is divisible by each of the factors of that number.

For example: $12$ is divisible by $6$

Factors of $6$ are $1,2,3$and $6$ 

Therefore, $12$ is also divisible by $1,2$ and $3$ 

If a number is divisible by two co-prime numbers, then it is divisible by their product also.

$160$ is divisible by $8$ and $5$ which are co-primes 

Product of $8$ and $5$ is $40$ 

Therefore, $160$ is also divisible by $40$ 

If two given numbers are divisible by a number, then their sum is also divisible by that number.

$15$ and $10$ are divisible by $5$ 

Sum of $15$ and $10$ is $25$ which is also divisible by $5$ 

If two given numbers are divisible by a number, then their difference is also divisible by that number

Difference of $15$ and $10$ is $5$ which is also divisible by $5$

Prime Factorization

The method of representing number as a product of its factors is called prime factorization.

For example: $36$ can be written as $2\times 2\times 3\times 3$, $2$ and $3$ are prime numbers.

Highest Common Factor

HCF of two or more number is the highest or greatest factor among all the common factors.

Factors of $60$ are $2\times 2\times 3\times 5$ 

Factors of $28$ are $2\times 2\times 3\times 7$ 

Common factors are: $2$ and $3$ 

Highest common factor is $3$

Lowest Common Multiple

LCM of two or more number is the lowest multiple among all the common multiples

Simply, product of the prime factors of two or more number is called LCM counted the maximum number of times they occur in any of the numbers.

Prime factorization of $30$ is $2\times 3\times 5$ 

Prime factorization of $4$ is $2\times 2$

LCM of $15$ and $4$ is $2\times 2\times 3\times 5=60$

Revision Notes for CBSE Class 6 Maths Chapter 3 - Free PDF Download

The chapter has seven exercises that include types of numbers, factors and their properties, multiples, prime and composite numbers, divisibility test of numbers, common multiples, common factors, prime factorisation, highest common factor, lowest common multiple and some practising problems based on LCM and HCF.

There are revision questions for practice related to all the topics mentioned above. These problems have been divided into 7 exercises from 3.1 to 3.7 for the students to identify the topics easily.

Introduction To CBSE Class 6 Maths Revision Notes

Introduction to CBSE Class 6 Maths Before you download the PDF, read some of those points that we have stated below. These are very basic revision notes and once you download the PDF, you will have more significant insights into the subject and there are high chances that you will perform better.

Playing With Numbers Class 6 Notes Revision notes that Vedantu provides will help you in understanding the core parts of that particular chapter and let you prepare well for the exam that you’ll be appearing in.

Class 6 Maths Chapter 3 Revision Notes

Our practise papers usually allow you to understand the pattern and the weightage of the subject and help you practice the same. In addition, we also add the important questions from the previous years so that you can master the subject before you appear for the examination.

A number is defined as an arithmetical value, expressed by words,  symbols, and figures. These numbers can be written either in single-digit format, double digits format, the three-digits format in the generalized form.

1. Types of Numbers

A number system is a system of writing the expression of numbers. According to the number system, there are different types of numbers. They are:

Prime numbers

Seven numbers

Odd numbers

Whole numbers

Natural numbers

Composite numbers

A factor of a number is a divisor of the number itself.

Example: 3, 4, 6, 9, 12, and 36 are the factors of 36.

3. Properties of Factors

1 is a factor of every number.

Every number is a factor of itself.

Every factor of a number is an exact division of that number.

Every factor of a given number is greater than or equal to the number.

4. Perfect Numbers

A perfect number is one of the types of numbers that has the sum of all the factors equal to twice the number.

Example: Factors of 56: 1, 2, 4, 7, 14, 28, and 56

Here, 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 x 8

Therefore, the sum of factors of 28 is equal to twice the number of 28.

5. Multiples

Multiples of a number are those numbers that we get on multiplying the number by an integer.

Examples: Multiples of 3 are 6,9,12,15,18 etc.

6. Properties of Multiples

There are infinite multiples of a given number.

Every number is a multiple of itself.

7. Prime Numbers

The numbers whose factors are 1 and the number itself are called Prime numbers.

Example: 2, 3, 5, 7 etc.

8. Composite Numbers

Numbers having multiple factors are called Composite numbers.

Example: 4, 6, 8 etc.

Divisible by 2 or 5 or both 2 and 5.

9. Divisibility Tests

Divisibility Test for 2

Divisibility Test for 4

Divisibility Test for 3

Divisibility Test for 5

Divisibility Test for 8

Divisibility Test for 6

Divisibility Test for 7

Divisibility Test for 9

Divisibility Test for 10

Divisibility Test for 11

10. Common Factor

1. Common Multiples

Why Refer To Vedantu For CBSE Class 6 Maths Revision Notes PDF?

We provide materials on NCERT Solutions for Class 6 Chapter 3 Playing with numbers in an accessible format.

Apart from this, we also provide notes, question papers and other learning materials in PDF format, which you can download and access offline as well. Also, by solving sample papers and previous year question papers through our website, you will get an idea of the exam pattern for Chapter 3 that will work as a helping hand for you in standing ahead in the exam preparation.

Expert Tips on CBSE Class 6 Exam Preparation

Have a positive attitude towards the exam

Set a deadline for each topic. This will help to finish all the subjects within the time.

After you have completed studying, you must revise all that you have already studied. 

Set your studying schedule and pick a peaceful place to study.

Set some time to refresh your memory. So, do some engaging activities regularly.

Ensure that you have enough sleep time

Before the exam, do not read any new topic rather stay stress-free, relaxed and calm while answering the questions.

Vedantu's "Playing With Numbers" Class 6 Notes for CBSE Maths Chapter 3 provide a comprehensive and valuable resource for students. The free PDF download offers an excellent opportunity for learners to enhance their mathematical skills in an engaging manner. The notes cover fundamental concepts, techniques, and practical examples, enabling students to grasp the topic with clarity. Vedantu's commitment to quality education is evident through these well-structured and accessible materials. By utilizing these resources, students can develop a solid foundation in number theory and problem-solving, empowering them to tackle more advanced mathematical challenges with confidence. Overall, Vedantu's Class 6 Notes serve as an invaluable aid in fostering a love for mathematics and promoting academic success.

FAQs on Playing With Numbers Class 6 Notes CBSE Maths Chapter 3 (Free PDF Download)

Q1. Does Vedantu Charge You Any Amount of Money to Access the Revision Notes?

Ans: No. Vedantu’s Class 6 Maths Chapter 3 notes are available free of cost. In order to help most students prepare for this subject and score good marks in your Examinations. Notes on playing with numbers class 6 can be downloaded free of cost from Vedantu’s Website. 

Q2. How Can Vedantu’s Chapter 3 Class 6 Maths Playing with Numbers Notes Help You?

Ans: Playing with numbers, class 6 notes of Vedantu provides will help you in:

Understanding the core parts of that particular chapter 

Let you prepare well for the exam beforehand. 

Practice papers can help you to know the pattern and the weightage of the subject. 

Vedantu has added some important questions from the previous years so that you can master the subject before you appear for the examination.

Q3. How to Make the Best Utilization of Study Time? List Out Some Resolutions and Strategies. 

Ans : Here are some effective time management tips for CBSE Class 6 students:

Study in shorter bursts

Do not do multitasking

Make a project plan

It would help if you start your assignments as soon

Set goals for study

Remove all kinds of distractions

Use an agenda

Build  a master schedule

4. What are the different types of numbers that are discussed in Chapter 3 of the CBSE Class 6 Maths textbook?

The different types of numbers that are discussed in Chapter 3 of the CBSE Class 6 Maths textbook are natural numbers, whole numbers, integers, and rational numbers.

Natural numbers are the numbers that we use for counting. They are the numbers from 1 to infinity.

Whole numbers are the numbers that include natural numbers and zero. They are the numbers from 0 to infinity.

Integers are the numbers that include whole numbers, negative whole numbers, and zero. They are the numbers from negative infinity to infinity.

Rational numbers are the numbers that can be expressed as a fraction of two integers. They are the numbers from negative infinity to infinity.

5. What is the difference between a prime number and a composite number?

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A composite number is a natural number that is not a prime number.

For example, 2 is a prime number because it is greater than 1 and it is not a product of two smaller natural numbers. 6 is a composite number because it is a product of two smaller natural numbers, 2 and 3.

NCERT Solutions

Cbse links for class 6.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers

NCERT Solutions for class 6 maths chapter 3 Playing With Numbers will help students study the topics, such as multiples, divisor, factors, and the identification of factors and multiples. In the previous two chapters, we studied whole numbers and natural numbers. With the help of this chapter, we will take a step ahead and learn the meaning of factors and multiples of a number. NCERT Solutions Class 6 maths chapter 3 consists of activities related to these concepts that make learning super easy.

With the help of the exercise questions, students will be able to find out the factors of a number using different methods. They will also be able to comprehend the application of these concepts in their day-to-day lives. Class 6 Maths NCERT Solutions Chapter 3 Playing with Numbers has a total of 7 exercises. With the help of this article, we will do an in-depth analysis of NCERT Solutions Class 6 Maths Chapter 3, and also you can find some of these in the exercises given below.

• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.1
• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.2
• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.3
• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.4
• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.5
• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.6
• NCERT Solutions Class 6 Maths Chapter 3 Ex 3.7

NCERT Solutions for Class 6 Maths Chapter 3 PDF

One of the key concepts covered in the NCERT solutions class 6 maths is finding the factors of a number in a stepwise manner. The only way students can get a good grasp of the concepts is by solving all the questions given in this coursebook. The NCERT Solutions for Class 6 Maths Chapter 3 are free to download using the links given below:

☛ Download Class 6 Maths NCERT Solutions Chapter 3 Playing with Numbers

NCERT Class 6 Maths Chapter 3   Download PDF

The best way to get strong fundamentals in maths is by practicing many questions on a regular basis. Thus, students need to visit the above links from time to time and revise all the questions. Numbers are everywhere, be it time, date, year, and weather; we use numerals to count things. We utilize numbers for counting money, measurements , phone numbers, phone passwords, locks, reading, page numbers, and TV channels. Engineers utilize numbers in their calculations when creating structures and roadways. They are also used by doctors to check blood counts and administer medications. With such wide applications of numbers , it is important for us to study the numbers in detail. An elaborate analysis of NCERT Solutions Class 6 Maths Chapter 3 is given below :

• Class 6 Maths Chapter 3 Ex 3.1 - 4 Questions
• Class 6 Maths Chapter 3 Ex 3.2 - 9 Questions
• Class 6 Maths Chapter 3 Ex 3.3 - 6 Questions
• Class 6 Maths Chapter 3 Ex 3.4 - 7 Questions
• Class 6 Maths Chapter 3 Ex 3.5 - 12 Questions
• Class 6 Maths Chapter 3 Ex 3.6 - 3 Questions
• Class 6 Maths Chapter 3 Ex 3.7 - 11 Questions

☛ Download Class 6 Maths Chapter 3 NCERT Book

Topics Covered: The topics covered under class 6 maths NCERT solutions chapter 3 are multiples , divisors , factors , identification of multiples, and factors. We will also learn how to determine if a number is prime or composite using the factors. Apart from that, we will explore how to find the HCF and LCM using the factors method.

Total Questions: Class 6 maths chapter 3 Playing with Numbers has 52 questions in total out of which 30 can be classified as easy short answer sums, 15 are long answer type problems while the other 7 are complex problems.

List of Formulas in NCERT Solutions Class 6 Maths Chapter 3

NCERT solutions class 6 maths chapter 3 does not consist of any formulas however there are some important concepts discussed in the chapter related to finding the HCF, LCM, and factors of numbers. We will discuss these essential concepts in this section.

• A prime number is any number other than 1 that has only two factors: 1 and the number itself. Composite numbers are those that have more than two factors. Number one is neither composite nor prime.
• If two numbers are divisible by a number, their sum and difference are likewise divisible by the same number.
• The Highest Common Factor (HCF) of two or more numbers is the highest common factor among them.
• The Least Common Multiple (LCM) of two or more numbers is the smallest of their common multiples.

Important Questions for Class 6 Maths NCERT Solutions Chapter 3

FAQs on NCERT Solutions for Class 6 Maths Chapter 3

Why are ncert solutions class 6 maths chapter 3 important.

NCERT solutions class 6 Maths Chapter 3 are designed by subject experts from IIT and Cambridge university. This chapter will help you understand the prime role that different numbers and their multiples play in solving an equation. These solutions also include various questions based on the laws of divisibility which are explained in detail. The NCERT solutions class 6 maths chapter 3 are the perfect study material for class 6 students as it will help them review their answers and also provide a step-wise approach to solve all questions.

Do I Need to Practice all Questions Provided in Class 6 Maths NCERT Solutions Playing with Numbers?

It is crucial for the students to practice all the questions in NCERT Solutions Class 6 Maths Playing With Numbers. This will help them understand the concepts better and build confidence, thus enabling them to memorize formulas faster. The main highlight of this chapter is HCF and LCM, and it is essential to practice all of the questions related to these topics. All the problems cover a variety of subject matter, thus allowing students to get a better grasp of numbers.

What are the Important Topics Covered in NCERT Solutions Class 6 Maths Chapter 3?

All the topics covered in NCERT Solutions Class 6 Maths Chapter 3 are equally important. However, to streamline the studying process, students need to give ample time in preparing questions based on HCF, LCM, and factors. Additionally, they must also go through the entire theory of the chapter to understand the concepts better.

How Many Questions are there in Class 6 Maths NCERT Solutions Chapter 3 Playing With Numbers?

There are 52 questions in the NCERT Solutions Class 6 Maths Chapter 3 Playing With Numbers. These are divided into seven different exercises. Exercise 3.6 and 3.7 are the most important exercises from an examination perspective, covering important topics like the prime factors, HCF, and LCM of numbers. Since these concepts are new to students, they should engage in activities to understand these concepts in a more practical way.

What are the Important Formulas in NCERT Solutions Class 6 Maths Chapter 3?

Students will come across many important concepts in the NCERT Solutions Class 6 maths chapter 3. We do not have any important formulas in this chapter; however certain facts like every number is a factor and multiple will help them understand the prime role that different numbers and their multiples play in solving an equation. Students must go through all the questions and solve the examples in order to develop a rock-solid foundation.

How CBSE Students can utilize NCERT Solutions Class 6 Maths Chapter 3 effectively?

To effectively utilize the NCERT Solutions Class 6 Maths Chapter 3, kids must first go through the theoretical concepts and activities discussed in the chapter. Topics such as common factors and multiples, divisibility laws, greatest common factors, lowest common factors, etc., are introduced to the kids. Students will be able to understand prime and composite numbers, as well as their differences, provided they have a thorough understanding of the chapter. This will help students identify practical ways of solving a problem.

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NCERT Solutions for Class 6 Maths Chapter 6 2024

CBSE Board Class 6 Study Material

CBSE Class 6 English Syllabus 2023

NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers

CBSE 2023 Class 6 Exam Dates: Check Important Dates

CBSE Class 6 Social Science Objective Questions

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NCERT Solutions for Class 6 Maths Chapter 3

NCERT Solutions For Class 6 Maths Chapter 3: The third chapter of NCERT Class 6 Maths is Playing with Numbers. The NCERT Solutions for Class 6 Maths chapter 3 at Embibe has been designed as per the latest CBSE syllabus. With the step-by-step problem-solving methodology, students will understand the right approach to answering the questions. Moreover, they will learn the correct application of formulas and concepts to derive an answer quickly.

Students preparing for their Class 6 Maths exams must practice all the questions provided at the end of Chapter 3 in the textbook. The chapter deals with major topics like prime and composite numbers, factors and multiples and more. There are 500+ practice questions at Embibe for this chapter that will help students boost their exam preparation. Continue reading for more information on NCERT Solutions for Class 6 Maths Chapter 3.

NCERT Solutions for Class 6 Maths Chapter 3: Important Topics

Mathematics requires a strong foundation and clear concepts to score better in exams. NCERT Solutions for Class 6 Maths Chapter 3 have been designed in an informative yet concise format. Students can refer to learning resources from Embibe, such as explainers and 3D videos , to get an in-depth understanding of the topics. The aim is to help students grasp the concepts while also having a fun time learning and practicing.

The practice module on Embibe allows students to solve various questions available for this chapter. There are 500+ questions on Embibe covering all the topics of Playing with Numbers to help students prepare for the exams in a better manner. Since Class 6 Maths Chapter 3 has numerous topics, practicing questions from each topic will gradually allow students to become thorough with the concepts.

NCERT Solutions for Class 6 Maths Chapter 3: Important Points to Remember

When preparing for the Maths exam of grade 6, students must ensure that they check the points to remember thoroughly. These are important points curated from the crucial topics of this chapter. These points will help simplify the entire chapter and ensure that students learn everything they can from their  textbooks  but faster and easier.

Below are some important points to remember from the NCERT Chapter 3 of Class 6 Maths:

• A factor of a number is that number which divides the number exactly.
• 1 is a factor of every number and is the only number that has exactly one factor.
• A multiple of a number is exactly divisible by the number.
• A number having no factor other than 1 and the number itself is called a Prime number. In other words, a Prime number has exactly two distinct factors, 1 and the number itself.
• A number having factors other than 1 and the number itself is called a Composite number.
• Primes occurring in pairs with a difference of two are called Twin primes.
• The product of H.C.F and L.C.M of two numbers equals their product. This result may not be true for more than two numbers.

Students can access more such important points for the chapter Playing with Numbers by clicking here .

NCERT Solutions for Class 6 Mathematics: All Chapters

Every chapter holds a special significance for students preparing for exams. Therefore, as soon as they are done with their learning and practicing from the chapters, they must turn to take mock tests from Embibe. When students take mock tests , they get to identify their strong and weak areas. Based on that, they will further be able to streamline their preparation and grasp the concepts in a better and easy-to-understand manner.

The NCERT Solutions for Class 6 Mathematics for all the chapters are mentioned below.

• 1st Chapter:  Knowing Our Numbers
• 2nd Chapter:  Whole Numbers
• 3rd Chapter:  Playing with Numbers
• 4th Chapter:  Basic Geometrical Ideas
• 5th Chapter:  Understanding Elementary Shapes
• 6th Chapter:  Integers
• 7th Chapter:   Fractions
• 8th Chapter:  Decimals
• 9th Chapter:  Data Handling
• 10th Chapter:  Mensuration
• 11th Chapter:  Algebra
• 12th Chapter:  Ratio and Proportion
• 13th Chapter:  Symmetry
• 14th Chapter:  Practical Geometry

FAQs on NCERT Solutions for Class 6 Maths Chapter 3

Below are the frequently asked questions on NCERT Solutions for Class 6 Maths Chapter 3:

Ans: Students can get NCERT Solutions for Class 6 Mathematics Chapter 3 from Embibe.

Ans: The NCERT Class 6 Mathematics Chapter 3 consists of 7 topics which are discussed on this page.

Ans: Embibe provides more than 500 questions for all the topics under the chapter – Playing With Numbers.

Ans: There are 14 chapters in NCERT Class 6 Maths.

Ans:  A number is divisible by 11 if the difference between the sum of its digits in odd places and the sum of its digits in even places (starting from the unit’s place) is either 0 or divisible by 11.

We hope that the article above on NCERT Solutions for the Class 6 Mathematics Chapter 3 helps to improve your preparation strategy. For any further updates on CBSE Class 6 exams, subscribe to Embibe .

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NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. It helps the students to understand slowly and to get practice well to become perfect and again a good score in their examination.

These materials are prepared based on Class 6 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 6 Solutions Maths Chapter 3 Playing With Numbers are in accordance with the latest CBSE guidelines and marking schemes

Class 6 Maths Chapter 3 Exercise 3.1 Solutions

Class 6 Maths Chapter 3 Exercise 3.2 Solutions

Class 6 Maths Chapter 3 Exercise 3.3 Solutions

Class 6 Maths Chapter 3 Exercise 3.4 Solutions

Class 6 Maths Chapter 3 Exercise 3.5 Solutions

Class 6 Maths Chapter 3 Exercise 3.6 Solutions

Class 6 Maths Chapter 3 Exercise 3.7 Solutions

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NCERT Solutions for Class 6 Maths Chapter 3 Free PDF Download

Ncert solutions for class 6 maths chapter 3 – playing with numbers.

While preparing for their examinations, students need to focus not only on concepts but also practice questions, especially in Mathematics. Now the NCERT textbook itself has exercises that provide the students with plenty of varied practice questions. So we are now presenting the students not only with the answers but with comprehensive solutions to these questions in our NCERT Solutions for Class 6 Maths Chapter 3 – Playing With Numbers.

Toppr’s NCERT Solutions for Class 6 Maths Chapter 3 – Playing With Numbers is focused not only on arriving at the answer but also explaining to the students all the steps involved. The main focus is on explanation and conceptual clarity rather than just arriving at the correct answer. Our experts have carefully curated various materials and complied the most comprehensive and easy-to-understand solutions for the benefit of the students.

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Download NCERT Solutions for Class 6 Maths here.

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CBSE Class 6 Maths Chapter 3 – Playing With Number NCERT Solutions

Now Playing with Numbers is one of the most interesting chapters of Class 6 Mathematics. It has many interesting concepts to cover from factors to prime numbers to LCM and HCF. All of these concepts are tested by interesting numerical and word problems in 7 different exercises. And in NCERT Solutions for Class 6 Maths Playing With Numbers, we cover all these seven exercises.

Sub-topics covered under NCERT Solutions for Class 6 Maths Chapter 3

1 – general form of a number.

In this topic, we will see the general form of two, three and four-digit numbers. We will also see how to form various numbers from any number of given digits. There are exercises where we will learn the mathematical functions of reversing three and four-digit numbers.

2- Prime and Composite Numbers

We will be introduced to the concept of a prime number and composite numbers. Students are also taught how to identify a number as either a prime number or a composite number.

3 – Prime Factors of a Number

We will revisit the concept of factorization. Then students will learn the meaning of prime factorization and how to find the prime factors of any given number, i.e. break down a number into its very basic prime factors.

4 – Divisibility Tests

This subtopic teaches students to check divisibility of a number without actually dividing the number. We will learn some smart and fun divisibility rules and various divisibility tests for the digits 2, 3, 4, 5, 6, 7, 8, 9 and 11. We will also learn some tricks for the divisibility of higher numbers like 13 and 17.

5- HCF and LCM

Students are introduced to the concept of the Highest Common Factor (HCF). And they are also taught how to find HCF of numbers by the listing method and the come comprehensive prime factorization method. Then we move on to Lowest Common Multiple (LCM) and finding LCM by prime factorization and division method.

You can download NCERT Solutions for Class 6 Maths Chapter 6 PDF by clicking on the download button below

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CBSE Class 6 Maths Revision Notes Chapter 3

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CBSE Class 6 Mathematics Chapter 3 Revision Notes – Playing With Numbers

Extramarks’ Class 6 Mathematics Chapter 3 Notes are curated by subject matter experts in pointers to help students grasp the chapter’s concepts easily. These notes provide all of the major points in the chapter in a well-structured manner. With these notes, students can develop conceptual clarity and a better understanding of the topics.

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Revision Notes For CBSE Class 6 Mathematics Chapter 3 

Access class 6 mathematics chapter 3 notes – playing with numbers, revision notes for cbse class 6 mathematics chapter 3.

CBSE Class 6 Mathematics Chapter 3 Notes will help students revise the core concepts in the shortest time. All the concepts have been illustrated with suitable examples so that students can understand them easily. These notes are available on the website. Students can access these notes at their convenience.

Introduction To CBSE Class 6 Mathematics Chapter 3 Revision Notes

The revision notes on Chapter 3 “Playing With Numbers” of Class 6 Mathematics deal with the basic concepts of factors, multiples, prime numbers, composite numbers, and the rules of divisibility along with HCF and LCM. All the terms associated with this chapter are explained in an easy way. Students will be able to solve problems with confidence once they go through these notes properly. 

Class 6 Mathematics Chapter 3 Revision Notes

A number is an arithmetical value that can be expressed using words, symbols, and numbers. These numbers can be expressed in the generalised form as single-digit, double-digit, or three-digit numbers.

The topics covered in Class 6 Mathematics Chapter 3 Notes include :

Types of Numbers: A system for writing numerical expressions is referred to as a number system. There are various types of numbers in the number system, which are:-

• Composite numbers
• Natural numbers
• Odd numbers
• Prime numbers
• Seven numbers
• Whole numbers

Factor: If a number divides another number exactly, then the divisor is called a factor of that number. For example, if 10 is divided by 2 or 5 it leaves no remainder. Therefore, 2 and 5 are factors of 10. 

Properties of a Factor

• Every number is exactly divisible by its factor.
• 1 is a factor of every number as it divides every number evenly.
• Every number is a factor of itself as every number is exactly divisible by itself.
• Factors must be less than or equal to the given number.
• Every number has a fixed number of factors.

Multiple: If a number is multiplied by an integer, the product is called the multiple of that number. For example, the multiples of 2 are 4, 6, 8, 10, 12 etc. 

Properties of a Multiple

• Every number is a multiple of itself.
• Multiples can never be smaller than the number itself.
• The number of multiples of a given number is infinite.

Difference between Factor and Multiple

• A factor is an exact divisor of a given number, whereas, a multiple is the product of a given number and an integer.
• Factors can be less than or equal to the given number. However, multiples are greater than or equal to the given number.
• The number of factors of a given number is limited, but the number of multiples of a given number is infinite.

Common Factor and Common Multiple: A factor which is common in two or more numbers is called a common factor. Similarly, a multiple which is common in two or more numbers is called a common multiple.

• Consider two numbers, 8 and 10. The factors of 8 are 1, 2, 4, and 8. Factors 10 are 1, 2, 5, and 10. Therefore, 2 is a common factor of both numbers.
• The multiples of 5 are 10, 15, 20, 25, 30, 35, 40 etc. The multiples of 7 are 14, 21, 28, 35, 42, 49, etc. The multiple 35 is common in both cases. Hence, 35 is a common multiple of 5 and 7.
• If two or more two numbers have only one common factor and that is 1, then the numbers are called co-prime numbers. For example, 2, 5, and 41 are co-prime numbers.

Prime Numbers: Prime numbers are those numbers which are divisible by 1 and that number only. For example, 2, 3, 5, 7, 11 etc. are prime numbers.

• 1 is not a prime number.
• 2 is the smallest prime number.
• 2 is the smallest even prime number.
• 3 is the smallest odd prime number.
• All prime numbers are odd numbers except 2.

Composite Numbers: Composite numbers are those which are divisible by more than two factors. For example, consider the number 6. It is divisible by 1, 2, 3, and itself. So, it has four factors. Therefore, it is a composite number.

• 1 is not a composite number since it has one factor only, that is, 1.
• Therefore, 1 is neither a prime number nor a composite number.

Perfect Numbers: A perfect number is one where the total of all its factors is twice the number.

For example, 1, 2, 4, 7, 14, 28, and 56 are the factors of 56.

Here, 1 + 2 + 4 + 7 + 14 + 28 = 56, which also equals to 2 x 28

As a result, the total of 28 factors equals double the number of 28.

Rules Of Divisibility

Divisibility by 10

• A number is divisible by 10 if it has zero at its ones place.
• For example, 20, 30, 40, 100, 300, and 1000 all are divisible by 10.

Divisibility by 5

• A number is divisible by 5 if it has zero or five at its ones place.
• For example, 10, 15, 20, 25, 55, 75, 95, etc., are divisible by 5.

Divisibility by 2

• A number is divisible by 2 if it has an even number at ones place.
• In other words, the numbers which have 2, 4, 6, or 8 in their ones place are divisible by 2.
• For example, 12, 24, 36, 88, etc., are divisible by 2.

Divisibility by 3

• A number is divisible by 3 if the sum of its digits is exactly divisible by 3.
• For example, suppose 102 is a given number. The sum of its digits 1, 0 and 2 is divisible by 3, ie., 1 + 0 + 2 = 3, which is divisible by 3. Therefore, the number 102 is divisible by 3.

Divisibility by 4

• A number with three or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.
• For example, 412, 1020, 5028 etc. are divisible by 4 because the numbers formed by the digits of tens place and ones place are divisible by 4.
• Therefore, a number with three or more digits is divisible by 4 if the number formed by its last two digits is a multiple of 4.
• In the case of single-digit or double-digit numbers, divisibility has to be checked by actual division. 

Divisibility by 6

• A number is divisible by 6 if it is divisible by both 2 and 3.
• For example, the number 36 is divisible by both 2 and 3. So, it is also divisible by 6.

Divisibility by 8

• A number with three or more digits is divisible by 8 if the number formed by the last three digits is divisible by 8.
• For example, 2000, 2416, 3104, etc. are divisible by 8.
• Divisibility for two- or three-digit numbers must be checked by actual division.

Divisibility by 9

• A number is divisible by 9 if the sum of its digits is divisible by 9.
• For example, consider the number 198. The sum of its digits 18 is divisible by 9.
• Therefore, the number 198 is divisible by 9.

Divisibility by 11

• A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is zero or exactly divisible by 11 itself.
• For example, consider a number, say 592845.
• The sum of the digits at odd places = 9 + 8 + 5 = 22.
• The sum of the digits at even places = 5 + 2 + 4 = 11.
• The difference between the sums = 22 – 11 = 11.
• 11 is divisible by itself.
• Therefore, the number 592845 is also divisible by 11.

Some More Rules of Divisibility

• When a given number is divisible by another number, then the given number must be divisible by all the factors of the divisor.
• For example, 24 is divisible by 12.
• The factors of 12 are 1, 2, 3, 4, 6, and 12.
• Then 24 is also divisible by 2, 3, 4, and 6.
• If any two numbers are divisible by a certain number, then the sum of the two numbers is also divisible by the certain divisor.
• For example, 10 and 25 are divisible by 5.
• Therefore, the sum of 10 and 25, that is, 35 is also divisible by 5.
• If two co-prime numbers divide a given number exactly, then their product also divides the given number exactly.
• For example, 105 is divisible by the co-prime numbers 5 and 7.
• Then 105 is also divisible by the product of 5 and 7, that is, 35.
• If two numbers are divisible by a certain divisor, then their difference is also divisible by that divisor.
• For example, 20 and 30 are divisible by 5.
• Then the difference between 30 and 20, 10, is also divisible by 5.

Prime Factorisation: The method of expressing a number as a product of its prime factors is called prime factorisation.

• For example, 24 can be written as 2 × 2 × 2 × 3. 2 and 3 are the prime factors.

Highest Common factor (HCF) and Least Common factor (LCM)

• The HCF is the highest or greatest factor common in two or more numbers.
• The LCM is the smallest multiple commons in two or more numbers.
• For example, 10 and 15 are the given numbers.
• Prime factorisation of 10 = 1 × 2 × 5.
• Prime factorisation of 15 = 1 × 3 × 5.
• Therefore, the HCF = 1 × 5 = 5.
• And, the LCM = 1 × 2 × 3 × 5 = 30.

Why Refer to Extramarks for CBSE Class 6 Mathematics Revision Notes?

With the right study materials and practice, students can score better marks in Mathematics. Extramarks is an ideal study partner as students can easily access concise and precise Class 6 Mathematics Revision Notes from the website. They can refer to these notes and gain conceptual clarity in every topic and answer every question with confidence. 

The notes are prepared meticulously by subject matter experts to help students perform better in exams. Every topic is illustrated with examples so that they can understand the logic behind the statements. All of the major points given in the revised CBSE syllabus for Mathematics are covered in detail.

Expert Tips on CBSE Class 6 Exam Preparation

Here are some tips for students to improve their Class 6 exam preparations:

• Time Management 

Making a schedule for studies helps students utilise the maximum time before the exam. They can revise the points that they have read and practised before answering the questions. However, they should also take some time to relax. During these study breaks, students can meditate, create art, or listen to music.

Time management is also crucial in the exam hall. Students must first read the questions and then attempt the questions they are most confident in. It is important to not get stuck on a question. Leave it for later inspection and move on to the next question.  An additional tip is to practise writing neatly at a fast pace to make answers presentable.

• Write the Points 

Practice makes one perfect. Therefore, students may write the points in their own understanding so that it is easier to remember them. It will also help them understand how much time should be given to each question or topic in the exam.

• Make Your Own Diagrams

Visual representation is always helpful in understanding a topic. Drawing small diagrams will help students grasp all of the ideas in one go. Mind maps can be used to understand the connections between two concepts. So, students can make their own diagrams and glance at them before entering the exam hall. 

• Write with Confidence

Many students often score poor marks in exams despite having strong preparation. The main reason for it is a lack of confidence. Students often become stressed and start making mistakes. The key here is to write with confidence. With good time management, students can take the last 10-15 minutes to review their answers and check if the correct question numbers are written beside the answers before submitting the answer script.

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FAQs (Frequently Asked Questions)

1. write the first three multiples of 12..

The first three multiples of 12 are 12, 24, and 36.

2. Are 5 and 11 co-prime numbers?

The prime factorisation of 5 and 11 are 1 × 5 and 1 × 11 respectively. 1 is their only common factor. Therefore, 5 and 7 are co-prime numbers.

3. Find the common factors of the co-prime numbers 29 and 47.

All the co-prime numbers have only one common factor, that is, 1. So, the answer will be 1.

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NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers

NCERT Solutions for Class 6 Maths Chapter 3 are given below in an easy-to-understand way for students of Class 6. Check out the detailed NCERT solutions for Class 6 Maths Chapter 3 on this blog.

January 16, 2024

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NCERT Solutions for Class 6 Maths Chapter 3

NCERT Solutions for Class 6 Maths Chapter 3: The NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers are beneficial for exam readiness as they cover various questions in the seven exercises of this chapter. At PhysicsWallah, subject experts crafted these solutions to offer the best methods for problem-solving. 

They serve as excellent study materials for CBSE Class 6 students aiming for good marks in the Maths Examination. The chapter delves into multiples, divisors, factors, and how to recognize them, and introduces concepts like HCF and LCM. Resolving the problems in this chapter aids students in understanding number-related topics easily.

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NCERT Solutions for Class 6 Maths Chapter 3 Overview

When students enter the 6th standard, they encounter the diverse syllabus of NCERT Solutions for Class 6 Maths Chapter 3, which includes various topics. The chapter, Playing with Numbers, concentrates on teaching multiples and divisors. 

As the chapter unfolds, students learn about common factors, multiples, divisibility rules, highest common factors, lowest common factors, etc. A thorough understanding of the chapter helps students discern prime and composite numbers. Students can download NCERT Class 6 Maths and NCERT Class 6 Science to revise the complete syllabus and score higher marks.

NCERT Solutions for Class 6 Maths Chapter 3 PDF Download

The chapter covers factors, multiples, prime and composite numbers, divisibility tests, common factors, common multiples, prime factorization, highest common factor, lowest common multiple, and related problems. Specific problems related to these topics are divided into 7 exercises for easy identification.

By using NCERT solutions for Class 6 Maths Chapter 3, students can get ready for their exams more easily. The solved examples given here assist students in figuring out the steps for solving similar problems. Additionally, these examples help students grasp fundamental knowledge that will be handy in the future.

These solutions aid in understanding the important role played by various numbers and their multiples in solving equations. The formulas introduced in this chapter are basic equations that will become handy when students progress to solving more complicated problems.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.1

1. write all the factors of the following numbers:.

(a) 24 = 1 x 24

24 = 2 x 12

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.

(b) 15 = 1 x 15

The factors of 15 are: 1, 3, 5, and 15.

(c) 21 = 1 x 21

The factors of 21 are: 1, 3, 7, and 21.

(d) 27 = 1 x 27

The factors of 27 are: 1, 3, 9, and 27.

(e) 12 = 1 x 12

The factors of 12 are: 1, 2, 3, 4, 6, and 12.

(f) 20 = 1 x 20

20 = 2 x 10

The factors of 20 are: 1, 2, 4, 5, 10, and 20.

(g) 18 = 1 x 18

The factors of 18 are: 1, 2, 3, 6, 9, and 18.

(h) 23 = 1 x 23

The factors of 23 are: 1 and 23.

(i) 36 = 1 x 36

36 = 2 x 18

36 = 3 x 12

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

2. Write the first five multiples of:

(a) First five multiples of 5 are:

Therefore, five multiples of 5 are: 5, 10, 15, 20, and 25.

(b) First five multiples of 8 are:

8 x 2 = 16;

8 x 3 = 24;

8 x 4 = 32;

Therefore, five multiples of 8 are: 8, 16, 24, 32, and 40.

(c) First five multiples of 9 are:

9 x 2 = 18;

9 x 3 = 27;

9 x 4 = 36;

Therefore, five multiples of 9 are: 9, 18, 27, 36, and 45.

3. Match the items in column 1 with the items in column 2.

Column 1                                                                                                         Column 2

(i) 35                                                                                                         (a) Multiple of 8

(ii) 15                                                                                                        (b) Multiple of 7

(iii) 16                                                                                                       (c) Multiple of 70

(iv) 20                                                                                                       (d) Factor of 30

(v) 25                                                                                                        (e) Factor of 50

(i) 35 (b) Multiple of 7

(ii) 15 (d) Factor of 30

(iii) 16 (a) Multiple of 8

(iv) 20 (f) Factor of 20

(v) 25 (e) Factor of 50

4. Find all the multiples of 9 up to 100.

9 x 10 = 90

9 x 11 = 99

Therefore, all the multiples of 9 up to 100 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.

CBSE Board Exam Centre List 2024

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.2

1. what is the sum of any two (a) odd numbers (b) even numbers.

(a) The sum of any two odd numbers is an even number.

Examples: 5 + 3 = 8

15 + 13 = 28

(b) The sum of any two even numbers is an even number

Examples: 2 + 8 = 10

12 + 28 = 40

2. State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(c) The product of three odd numbers is odd.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

(a) False. The sum of three odd numbers is odd.

Example: 7 + 9 + 5 = 21 i.e odd number

(b) True. The sum of two odd numbers and one even number is even.

Example: 3 + 5 + 8 = 16 i.e., is an even number.

(c) True. The product of three odd numbers is odd.

Example: 3 × 7 × 9 = 189 i.e., is an odd number.

(d) False. If an even number is divided by 2, the quotient is even.

Example: 8 ÷ 2 = 4

(e) False, All prime numbers are not odd.

Example: 2 is a prime number, but it is also an even number.

(f) False. Since 1 and the number itself are factors of the number

(g) False. The sum of two prime numbers may also be an odd number

Example: 2 + 5 = 7 i.e., an odd number.

(h) True. 2 is the only even prime number.

(i) False. Since 2 is a prime number.

(j) True. The product of two even numbers is always even.

Example: 2 × 4 = 8 i.e., even number.

3. The numbers 13 and 31 are prime numbers. Both these numbers have the same digits, 1 and 3. Find such pairs of prime numbers up to 100.

The prime numbers with the same digits up to 100 are as follows:

4. Write down separately the prime and composite numbers less than 20.

2, 3, 5, 7, 11, 13, 17 and 19 are the prime numbers less than 20

4, 6, 8, 9, 10, 12, 14, 15, 16 and 18 are the composite numbers less than 20

5. What is the greatest prime number between 1 and 10?

2, 3, 5 and 7 are the prime numbers between 1 and 10. 7 is the greatest prime number among them.

6. Express the following as the sum of two odd primes.

(a) 3 + 41 = 44

(b) 5 + 31 = 36

(c) 5 + 19 = 24

(d) 5 + 13 = 18

7. Give three pairs of prime numbers whose difference is 2. [Remark: Two prime numbers whose difference is 2 are called twin primes].

The three pairs of prime numbers whose difference is 2 are

8. Which of the following numbers is prime?

1 × 23 = 23

23 × 1 = 23

Therefore 23 has only two factors 1 and 23. Hence, it is a prime number.

1 × 51 = 51

3 × 17 = 51

Therefore 51 has four factors 1, 3, 17 and 51. Hence, it is not a prime number, it is a composite number.

1 × 37 = 37

37 × 1 = 37

Therefore 37 has two factors 1 and 37. Hence, it is a prime number.

1 × 26 = 26

2 × 13 = 26

Therefore 26 has four factors 1, 2, 13 and 26. Hence, it is not a prime number, it is a composite number.

9. Write seven consecutive composite numbers less than 100 so there is no prime number between them.

Seven composite numbers between 89 and 97, both of which are prime numbers, are 90, 91, 92, 93, 94, 95 and 96

Numbers                                                                                                          Factors

90                                                                                                       1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 

91                                                                                                        1, 7, 13, 91

92                                                                                                        1, 2, 4, 23, 46, 92

93                                                                                                        1, 3, 31, 93

94                                                                                                        1, 2, 47, 94

95                                                                                                        1, 5, 19, 95

96                                                                                                        1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48

 10. Express each of the following numbers as the sum of three odd primes:

(a) 3 + 5 + 13 = 21

(b) 3 + 5 + 23 = 31

(c) 13 + 17 + 23= 53

(d) 7 + 13 + 41 = 61

11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint: 3 + 7 = 10)

The five pairs of prime numbers less than 20 whose sum is divisible by 5 are

2 + 13 = 15

3 + 17 = 20

7 + 13 = 20

19 + 11 = 30

 12. Fill in the blanks:

(a) A number with only two factors is called a ______.

(b) A number with more than two factors is called a ______.

(c) 1 is neither ______ nor ______.

(d) The smallest prime number is ______.

(e) The smallest composite number is _____.

(f) The smallest even number is ______.

(a) A number with only two factors is called a prime number.

(b) A number with more than two factors is called a composite number.

(c) 1 is neither a prime number nor a composite number.

(d) The smallest prime number is 2

(e) The smallest composite number is 4

(f) The smallest even number is 2.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3

1. using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):.

2. Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:

(h) 31795072

72 are the last two digits. Since 72 is divisible by 4. Hence, 572 is also divisible by 4

572 are the last three digits. Since 572 is not divisible by 8. Hence, 572 is not divisible by 8

52 are the last two digits. Since 52 is divisible by 4. Hence, 726352 is divisible by 4

352 are the last three digits. Since 352 is divisible by 8. Hence, 726352 is divisible by 8

Since the last two digits are 00. Hence 5500 is divisible by 4

500 are the last three digits. Since 500 is not divisible by 8. Hence, 5500 is not divisible by 8

Since the last two digits are 00. Hence 6000 is divisible by 4

Since the last three digits are 000. Hence, 6000 is divisible by 8

59 are the last two digits. Since 59 is not divisible by 4. Hence, 12159 is not divisible by 4

159 are the last three digits. Since 159 is not divisible by 8. Hence, 12159 is not divisible by 8

60 are the last two digits. Since 60 is divisible by 4. Hence, 14560 is divisible by 4

560 are the last three digits. Since 560 is divisible by 8. Hence, 14560 is divisible by 8

84 are the last two digits. Since 84 is divisible by 4. Hence, 21084 is divisible by 4

084 are the last three digits. Since 084 is not divisible by 8. Hence, 21084 is not divisible by 8

72 are the last two digits. Since 72 is divisible by 4. Hence, 31795072 is divisible by 4

072 are the last three digits. Since 072 is divisible by 8. Hence, 31795072 is divisible by 8

Since the last two digits are 00. Hence, 1700 is divisible by 4

700 are the last three digits. Since 700 is not divisible by 8. Hence, 1700 is not divisible by 8

50 are the last two digits. Since 50 is not divisible by 4. Hence, 2150 is not divisible by 4

150 are the last three digits. Since 150 is not divisible by 8. Hence, 2150 is not divisible by 8

3. Using divisibility tests, determine which of the following numbers are divisible by 6:

(g) 1790184

Since the last digit of the number is 4. Hence, the number is divisible by 2

By adding all the digits of the number, we get 27, which is divisible by 3. Hence, the number is divisible by 3

∴ The number is divisible by both 2 and 3. Hence, the number is divisible by 6

Since the last digit of the number is 8. Hence, the number is divisible by 2

By adding all the digits of the number, we get 16 which is not divisible by 3. Hence, the number is not divisible by 3

∴ The number is not divisible by both 2 and 3. Hence, the number is not divisible by 6

Since the last digit of the number is 5, which is not divisible by 2. Hence, the number is not divisible by 2

By adding all the digits of the number, we get 15 which is divisible by 3. Hence, the number is divisible by 3

Since the last digit of the number is 3, which is not divisible by 2. Hence, the number is not divisible by 2

Since the last digit of the number is 2. Hence, the number is divisible by 2

By adding all the digits of the number, we get 20 which is not divisible by 3. Hence, the number is not divisible by 3

Since the last digit of the number is 0. Hence, the number is divisible by 2

By adding all the digits of the number, we get 27 which is divisible by 3. Hence, the number is divisible by 3

By adding all the digits of the number, we get 30 which is divisible by 3. Hence, the number is divisible by 3

Since the last digit of the number is 3. Hence, the number is not divisible by 2

By adding all the digits of the number, we get 19 which is not divisible by 3. Hence, the number is not divisible by 3

By adding all the digits of the number, we get 21, which is divisible by 3. Hence, the number is divisible by 3

By adding all the digits of the number, we get 23 which is not divisible by 3. Hence, the number is not divisible by 3

Benefits of NCERT Solutions for Class 6 Maths Chapter 3

Here are some of the main benefits of using NCERT Solutions for Class 6 Maths Chapter 3:

• The solutions are designed according to the exam pattern, aiding students in achieving good scores.
• All questions and answers are written in easy language.
• The answers to each question are clear and concise.
• All solutions are helpful and efficient in assisting students to score well.

NCERT Solutions for Class 6 Maths Chapter 3 FAQs

NCERT Class 6 Maths Chapter 3 focuses on playing with numbers, exploring concepts such as factors, multiples, and prime numbers.

Availing Chapter 3 Maths Class 6 NCERT Solutions is beneficial for comprehending fundamental mathematical concepts, ensuring a strong foundation for future topics.

Factors are numbers that completely divide a given number, while multiples are the result of multiplying a number by any integer.

Prime numbers have only two factors (1 and the number itself), whereas composite numbers have more than two factors.

Class 6 Maths Chapter 3 lays the groundwork for understanding essential concepts like factors and primes, forming a basis for advanced mathematical topics in higher studies.

NCERT Solutions for Class 6 Science Chapter 12 Electricity And Circuits

JKBOSE Exam Date 2024 OUT, Exam Schedule Class 10th, 12th

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Revision Notes on Playing with Numbers

The numbers which exactly divides the given number are called the Factors of that number.

As we can see that we get the number 12 by

1 × 12, 2 × 6, 3 × 4, 4 × 3, 6 × 2 and 12 ×1

1, 2, 3, 4, 6 and 12 are the factors of 12.

The factors are always less than or equal to the given number.

If we say that 4 and 5 are the factors of 20 then 20 is the multiple of 4 and 5 both.

List the multiples of 3

Multiples are always more than or equal to the given number.

Some facts about Factors and Multiples

1 is the only number which is the factor of every number.

Every number is the factor of itself.

All the factors of any number are the exact divisor of that number.

All the factors are less than or equal to the given number.

There are limited numbers of factors of any given number.

All the multiples of any number are greater than or equal to the given number.

There are unlimited multiples of any given numbers.

Every number is a multiple of itself.

Perfect Number

If the sum of all the factors of any number is equal to the double of that number then that number is called a Perfect Number .

Prime Numbers

The numbers whose only factors are 1 and the number itself are called the Prime Numbers .

Like 2, 3, 5, 7, 11 etc.

Composite Numbers

All the numbers with more than 2 factors are called composite numbers or you can say that the numbers which are not prime numbers are called Composite Numbers .

Like 4, 6, 8, 10, 12 etc.

Remark : 1 is neither a prime nor a composite number.

Sieve of Eratosthenes Method

This is the method to find all the prime numbers from 1 to 100.

Step 1: First of all cross 1, as it is neither prime nor composite.

Step 2: Now mark 2 and cross all the multiples of 2 except 2.

Step 3: Mark 3 and cross all the multiples of 3 except 3.

Step 4: 4 is already crossed so mark 5 and cross all the multiples of 5 except 5.

Step 5: Continue this process until all the numbers are marked square or crossed.

This shows that all the covered numbers are prime numbers and all the crossed numbers are composite numbers except 1.

Even and Odd Numbers

All the multiples of 2 are even numbers . To check whether the number is even or not, we can check the number at one's place. If the number at ones place is 0,2,4,6 and 8 then the number is even number.

The numbers which are not even are called Odd Numbers .

Remark: 2 is the smallest even prime number. All the prime numbers except 2 are odd numbers.

Tests for Divisibility of Numbers

1. Divisibility by 2:

If there are any of the even numbers i.e. 0, 2, 4, 6 and 8 at the end of the digit then it is divisible by 2.

Check whether the numbers 63 and 240 are divisible by 2 or not.

Solution: 

1. The last digit of 63 is 3 i.e. odd number so 63 is not divisible by 2.

2. The last digit of 240 is 0 i.e. even number so 240 is divisible by 2.

2. Divisibility by 3:

A given number will only be divisible by 3 if the total of all the digits of that number is multiple of 3.

Example  

Check whether the numbers 623 and 2400 are divisible by 3 or not.

1. The sum of the digits of 623 i.e. 6 + 2 + 3 = 11, which is not the multiple of 3 so 623 is not divisible by 3.

2. The sum of the digits of 2400 i.e. 2 + 4 + 0 + 0 = 6, which is the multiple of 3 so 2400 is divisible by 3.

3. Divisibility by 4:

We have to check whether the last two digits of the given number are divisible by 4 or not. If it is divisible by 4 then the whole number will be divisible by 4.

Check the number 23436 and 2582 are divisible by 4 or not.

1. The last two digits of 23436 are 36 which are divisible by 4, so 23436 are divisible by 4.

2. The last two digits of 2582 are 82 which are not divisible by 4 so 2582 is not divisible by 4.

4. Divisibility by 5:

Any given number will be divisible by 5 if the last digit of that number is ‘0' or ‘5'.

Check whether the numbers 2348 and 6300 are divisible by 5 or not.

Solution:  

1. The last digit of 2348 is 8 so it is not divisible by 5.

2. The last digit of 6300 is 0 so it is divisible by 5.

5. Divisibility by 6:

Any given number will be divisible by 6 if it is divisible by 2 and 3 both. So we should do the divisibility test of 2 and 3 with the number and if it is divisible by both then it is divisible by 6 also.

Check the number 342341 and 63000 are divisible by 6 or not.

1. 342341 is not divisible by 2 as the digit at ones place is odd and is also not divisible by 3 as the sum of its digits i.e. 3 + 4 + 2 + 3 + 4 + 1 = 17 is also not divisible by 3.Hence 342341 is not divisible by 6.

2. 63000 is divisible by 2 as the digit at ones place is even and is also divisible by 3 as the sum of its digits i.e. 6 + 3 + 0 + 0 + 0 = 9 is divisible by 3.Hence 63000 is divisible by 6.

6. Divisibility by 7:

Any given number will be divisible by 7 if we double the last digit of the number and then subtract the result from the rest of the digits and check whether the remainder is divisible by 7 or not. If there is a large number of digits then we have to repeat the process until we get the number which could be checked for the divisibility of 7.

Check the number 2030 is divisible by 7 or not.

Given number is 2030

1. Double the last digit, 0 × 2 = 0

2. Subtract 0 from the remaining number 203 i.e. 203 – 0 = 203

3. Double the last digit, 3 × 2 = 6

4. Subtract 6 from the remaining number 20 i.e. 20 - 6 = 14

5. The remainder 14 is divisible by 7 hence the number 203 is divisible by 7.

7. Divisibility by 8:

We have to check whether the last three digits of the given number are divisible by 8 or not. If it is divisible by 8 then the whole number will be divisible by 8.

Check whether the number 74640 is divisible by 8 or not.

The last three digit of the number 74640 is 640.

As the number 640 is divisible by 8 hence the number 74640 is also divisible by 8.

8. Divisibility by 9:

Any given number will be divisible by 9 if the total of all the digits of that number is divisible by 9.

Check whether the number 2320 and 6390 are divisible by 9 or not.

1. The sum of the digits of 2320 is 2 + 3 + 2 + 0 = 7 which is not divisible by 9 so 2320 is not divisible by 9.

2. The sum of the digits of 6390 is 6 + 3 + 9 + 0 = 18 which is divisible by 9 so 6390 is divisible by 9.

9. Divisibility by 10:

Any given number will be divisible by 10 if the last digit of that number is zero.

Check the number 123 and 2630 are divisible by 10 or not.

1. The ones place digit is 3 in 123 so it is not divisible by 10.

2. The ones place digit is 0 in 2630 so it is divisible by 10.

Common Factors and Common Multiples

What are the common factors of 25 and 55?

Factors of 25 are 1, 5.

Factors of 55 are 1, 5, 11.

Common factors of 25 and 55 are 1 and 5.

Find the common multiples of 3 and 4.

Common multiples of 3 and 4 are 0, 12, 24 and so on.

Co-prime Numbers

If 1 is the only common factor between two numbers then they are said to be Co-prime Numbers .

Check whether 7 and 15 are co-prime numbers or not.

Factors of 7 are 1 and 7.

Factors of 15 are 1, 3, 5 and 15.

The common factor of 7 and 15 is 1 only. Hence they are the co-prime numbers.

Some more Divisibility Rules

1. Let a and b are two given numbers. If a is divisible by b then it will be divisible by all the factors of b also.

If 24 is divisible by 12 then 24 will be divisible by all the factors of 12(i.e.2, 3, 4, 6) also.

2. Let a and b are two co-prime numbers. If c is divisible by a and b then c will be divisible by the product of a and b (ab) also.

If 24 is divisible by 2 and 3 which are the co-prime numbers then 24 will also be divisible by the product of 2 and 3 (2×3=6).

3. If a and b are divisible by c then a + b will also be divisible by c.

If 24 and 12 are divisible by 4 then 24 + 12 = 36 will also be divisible by 4.

4. If a and b are divisible by c then a-b will also be divisible by c.

If 24 and 12 are divisible by 4 then 24 -12 = 12 will also be divisible by 4.

Prime Factorisation

Prime Factorisation is the process of finding all the prime factors of a number.

There are two methods to find the prime factors of a number-

1. Prime factorisation using a factor tree

We can find the prime factors of 70 in two ways.

The prime factors of 70 are 2, 5 and 7 in both the cases.

2. Repeated Division  Method

Find the prime factorisation of 64 and 80.

The prime factorisation of 64 is 2 × 2 × 2 × 2 × 2 × 2.

The prime factorisation of 80 is 2 × 2 × 2 × 2 × 5.

Highest Common Factor (HCF)

The highest common factor (HCF) of two or more given numbers is the greatest of their common factors.

Its other name is (GCD) Greatest Common Divisor .

Method to find HCF

To find the HCF of given numbers, we have to find the prime factorisation of each number and then find the HCF.

Find the HCF of 60 and 72.

First, we have to find the prime factorisation of 60 and 72.

Then encircle the common factors.

HCF of 60 and 72 is 2 × 2 × 3 = 12.

Lowest Common Multiple (LCM)

The lowest common multiple of two or more given number is the smallest of their common multiples.

Methods to find LCM

1. Prime Factorisation Method

To find the LCM we have to find the prime factorisation of all the given numbers and then multiply all the prime factors which have occurred a maximum number of times.

Find the LCM of 60 and 72.

To find the LCM, we will count the common factors one time and multiply them with the other remaining factors.

LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 = 360

2. Repeated Division Method

If we have to find the LCM of so many numbers then we use this method.

Find the LCM of 105, 216 and 314.

Use the repeated division method on all the numbers together and divide until we get 1 in the last row.

LCM of 105,216 and 314 is 2 × 2 × 2 × 3 × 3 × 3 × 5 × 7 × 157 = 1186920

Real life problems related to HCF and LCM

There are two containers having 240 litres and 1024 litres of petrol respectively. Calculate the maximum capacity of a container which can measure the petrol of both the containers when used an exact number of times.

As we have to find the capacity of the container which is the exact divisor of the capacities of both the containers, i. e. maximum capacity , so we need to calculate the HCF.

The common factors of 240 and 1024 are 2 × 2 × 2 × 2. Thus, the HCF of 240 and 1024 is 16. Therefore, the maximum capacity of the required container is 16 litres.

What could be the least number which when we divide by 20, 25 and 30 leaves a remainder of 6 in every case?

As we have to find the least number so we will calculate the LCM first.

LCM of 20, 25 and 30 is 2 × 2 × 3 × 5 × 5 = 300.

Here 300 is the least number which when divided by 20, 25 and 30 then they will leave remainder 0 in each case. But we have to find the least number which leaves remainder 6 in all cases. Hence, the required number is 6 more than 300.

The required least number = 300 + 6 = 306.

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NCERT Solutions for Class 6 Maths

Get here Class 6 Maths NCERT Solutions, a Guide for 2024-25 final Exams Free access of the complete NCERT Solutions for Class 6 Maths, brought to you by Tiwari Academy are here. These solutions are crafted in simple format to align with the CBSE syllabus for the 2024-25 academic year and are available in both Hindi and English Medium. Our Class 6 Maths Solutions provide detailed answers to all questions in the Class 6 Maths NCERT textbook, making them an essential resource for students.

Revised NCERT Solutions of Class 6 Maths

Aiming to ace your Maths exam? Dive into these 12 chapters of tailored solutions and deepen your concept grasp. Click below for chapter-wise ‘NCERT Solutions Class 6 Maths’ by Tiwari Academy:

Chapter 1. Knowing Our Numbers Chapter 2. Whole Numbers Chapter 3. Playing With Numbers Chapter 4. Basic Geometrical Ideas Chapter 5. Understanding Elementary Shapes Chapter 6. Integers Chapter 7. Fractions Chapter 8. Decimals Chapter 9. Data Handling Chapter 10. Mensuration Chapter 11. Algebra Chapter 12. Ratio and Proportion Chapters for State Board Only Chapter 13. Symmetry Chapter 14. Practical Geometry

Class 6 NCERT solutions for Mathematics refer to solutions provided by Tiwari Academy for the mathematics textbook of the 6th grade in the National Council of Educational Research and Training (NCERT) curriculum in Bharat. Please Provide your Review and Feedback so that we can prove you a better solutions in all subjects. Students of class 6 can often benefit from the feedback and reviews of other users who have used Tiwari Academy’s resources for Maths. This can help in assessing the quality and effectiveness of the materials.

NCERT Solutions App for Class 6

The Class 6 Maths NCERT solutions cover various mathematical concepts and topics appropriate for students at the 6th-grade level. These solutions provide step-by-step explanations, examples, and exercises that help students grasp the fundamental mathematical principles and develop problem-solving skills.

Class 6 Maths Chapter Wise Tests

Similar to other classes NCERT solutions, Class 6 Maths NCERT solutions can be obtained through various methods such as the official NCERT website, educational websites, mobile apps, and printed guides. These solutions are designed to make learning mathematics easier and more effective for students in their early stages of education.

Making class 6 Maths study easier and more enjoyable involves adopting effective study strategies and techniques. Here are some tips to help you make class 6 Maths more manageable. Start with a clear understanding of the basic mathematical concepts. Ensure you have a solid foundation in addition, subtraction, multiplication, and division. Create a clean, organized, and comfortable study space with all the necessary materials like textbooks, notebooks, pens, and a calculator if needed.

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Modern Developments in Various Fields of Maths Modern mathematics includes numerous subfields like number theory, geometry, algebra, calculus, discrete mathematics, mathematical logic, set theory, statistics, and computational mathematics. Each of these areas has its unique focus and applications, contributing to the rich tapestry of the mathematical universe.

Ultimately, the best solutions are the ones that help you understand and excel in your studies. It will be helpful to try out a couple of different options to see which works best for you. When you encounter difficult math problems as part of your homework assignments, NCERT solutions can serve as a valuable resource. You can refer to them to check your answers, ensuring that you’ve solved the problems correctly. NCERT solutions at Tiwari Academy are aligned with the NCERT textbooks, which are commonly used in schools across Bharat. This consistency ensures that you are studying the topics that are part of your curriculum, helping you stay on track with your class lessons.

To prepare for exams, break down the math topics into smaller, manageable sections. Visual aids such as diagrams, charts, and graphs can help you understand and remember mathematical concepts more effectively. Math is a subject that requires consistent practice. Solve problems regularly to reinforce your understanding of concepts. Don’t hesitate to ask your teacher or classmates for help if you’re struggling with a particular concept or problem. There’s no shame in seeking assistance.

Tips to Score well in 6th Maths Testing is the best way to know about the preparation for exams. Follow the methods given here to get help after completing the chapter. Test yourself to be confident in exams. 6th Maths Chapter wise Tests Follow the Tips and Tricks to get maximum in class 6 Maths exams.

• Regular practice.
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• Apply all tricks you know to solve the questions.
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• Do not learn the solutions, learn only formulae.
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NCERT is known for producing high-quality educational materials. The solutions provided are accurate, reliable, and well-researched, making them a trustworthy source https://www.tiwariacademy.com for learning and revision. If you need to study independently or want to revisit a topic at your own pace, NCERT solutions Class 6 Maths allow you to do so effectively. You can work through problems and understand concepts without external assistance.

Ways to make Class 6 Maths NCERT Solutions easier for students

Mathematics is important to have a strong foundation in grade 6 mathematics core concepts. Get command with a good understanding of numerals, addition, subtraction, multiplication and division tables. Use physical objects such as blocks, numbers or coins to visualize and solve problems from Maths book. As you know that the syllabus is reduced for academic year 2024-25, which makes the subject seem much easier. Class 6 Maths forms the foundation for more advanced mathematical concepts you’ll encounter in higher classes. Using NCERT solutions to master these basics sets you up for success in future math courses. Tiwari Academy Class 6 Maths solution provides you a better way to solve questions.

Utilize online resources like educational websites, Maths games, and tutorials to make learning more engaging and interactive. Study with classmates or join a study group. Explaining concepts to others and discussing problems can deepen your understanding. Manage your study time wisely. Allocate specific time slots for math study and take short breaks to stay focused. Try to relate math problems to real-life situations. This can make math more relatable and interesting.

Here are some of the benefits of using NCERT Solutions for Class 6 Maths. These cover all of the important topics in the CBSE syllabus for Class 6 Maths . This ensures that students are well-prepared for their exams. NCERT Solutions are written in a clear and concise manner, making them easy for students to understand. This is especially important for young learners who are still developing their Maths skills.

NCERT Solutions are graded in difficulty, with the concepts introduced in a logical order. This helps students to build on their prior knowledge and to develop a deep understanding of the concepts. Format is made totally according to class 6th Maths curriculum 2024-25. The deleted exercises are removed from the 6th Maths NCERT solutions section. The chapter wise tests of class 6 Maths are given below:

Chapter 1. Knowing Our Numbers Chapter 2. Whole Numbers Chapter 3. Playing With Numbers Chapter 4. Basic Geometrical Ideas Chapter 5. Understanding Elementary Shapes Chapter 6. Integers Chapter 7. Fractions Chapter 8. Decimals Chapter 9. Data Handling Chapter 10. Mensuration Chapter 11. Algebra Chapter 12. Ratio and Proportion

NCERT Solutions include a variety of activities and exercises that help students to practice the concepts they have learned. This helps students to retain the information and to develop their problem-solving skills.

Regularly review and revise what you’ve learned. This reinforces your knowledge and helps you retain information for longer. Solve previous years’ question papers to become familiar with the exam pattern and types of questions you might encounter in class 6 math exams. Don’t study for long stretches without breaks. Short, regular breaks can help improve concentration and reduce fatigue. Remember that making math easier takes time and effort, so be patient with yourself. Celebrate your successes, no matter how small, and don’t be discouraged by challenges. With consistent practice and a positive attitude, you can make class 6 math more manageable and even enjoyable.

Tips to Prepare Class 6 Maths Exams Getting ready for your Class 6 Mathematics finals can be fun and exciting if you know how to study smartly. First, take a look at what you need to learn – your syllabus will have all the topics listed. Make a study plan that gives you enough time for each part of the syllabus. It’s important to really understand the ideas in Maths, not just remember them. Use your school books, watch some cool math videos online, and try out lots of practice exercises. Remember, the more you practice, the better you’ll get at mathematics. If something seems too hard, don’t worry – ask your teacher or friends to help you out.

Sharpen your problem-solving skills. Maths is all about figuring out how to use what you know in different situations. Try solving old test papers and questions from previous years. This will help you get used to the kind of questions that come in the exam and also teach you how to manage your time. Pay attention to how you solve each problem – the steps you take can be just as important as the answer. Studying with friends can be really helpful too, because when you explain things to someone else, it helps you understand them better.

Keep a happy and positive mindset. Don’t try to learn everything at once – take breaks and make sure you get plenty of sleep. A well-rested brain works better! The day before your exam, just go over your notes lightly and try to relax. Believe in yourself and the hard work you’ve put in. During the exam, read each question carefully, keep an eye on the time, and don’t spend too long on one question. Remember, being well-prepared and confident is the secret to doing great in your Class 6 Maths finals!

Use Class 6 Apps (Android and iOS)

To study through mobile or tablets, students may use Tiwari Academy’s offline apps given here. These are the best source for NCERT solutions during study. Focus on Class 6 Maths Test papers, NCERT Exemplar Solutions, problem solving skills rather than memorizing mathematical concepts. The NCERT textbook solutions of Class 6 Maths is available for new session following the revised syllabus.

Download class 6 Android or iOS for iPhone and iPad Offline and Online best apps for new curriculum 2024-25. NCERT Solutions App for Class 6 Maths are an essential resource for students who want to excel in their Maths exams and to develop a deep understanding of the concepts.

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Using Android and iOS apps for NCERT (National Council of Educational Research and Training) Solutions can offer several advantages for students and educators. NCERT solutions Apps for Class 6 Maths are an invaluable resource for learning, practicing, and mastering mathematical concepts. They help you build a strong foundation in mathematics, which is essential for academic success in this subject and beyond.

The time duration required to complete the class 6 mathematics course can vary depending on several factors, including the curriculum, the student’s learning pace, the quality of instruction, and individual circumstances. Generally, a full academic year is allocated for the completion of the class 6 mathematics syllabus in most educational systems. In many countries, class 6 is part of the primary or middle school curriculum, and students typically have one academic year to complete the mathematics course. This means that the curriculum is designed to be taught and learned over the course of that year.

NCERT Solutions Class 6 Maths & Main Points of All Chapters

Chapter 1: Knowing Our Numbers

The Class 6 Maths Chapter 1 Solutions includes Exercise 1.1 , which is based on comparing numbers.

Class 6 Maths Chapter 1 for CBSE Board Class 6 Maths Exercise 1.1 Class 6 Maths Exercise 1.2

Class 6 Maths Chapter 1 for State Boards Class 6 Maths Chapter 1 Exercise 1.1 Class 6 Maths Chapter 1 Exercise 1.2 Class 6 Maths Chapter 1 Exercise 1.3

Class 6 Maths Chapter 1 in Hindi Medium Class 6 Maths Exercise 1.1 in Hindi Class 6 Maths Exercise 1.2 in Hindi

Concepts of ascending and descending order, shifting the digits, using place value, face value and dealing with a large number of 6 or 7 digits. We should use commas in Indian or International system very carefully. Class 6 Maths Exercise 1.2 contains sums related to the word problem. The basic knowledge of Roman numbering along with the use of brackets is point of focus at the end of chapter 1 of Class 6 Mathematics.

Chapter 2: Whole Numbers

The NCERT Class 6 Maths Chapter 2 starts with the concepts of successor and predecessor. Class 6 Maths Exercise 2.1 describes the addition and subtraction of integers using Number Line.

Class 6 Maths Chapter 2 for CBSE Board Class 6 Maths Exercise 2.1

Class 6 Maths Chapter 2 for State Boards Class 6 Maths Chapter 2 Exercise 2.1 Class 6 Maths Chapter 2 Exercise 2.2 Class 6 Maths Chapter 2 Exercise 2.3

Class 6 Maths Chapter 2 in Hindi Medium Class 6 Maths Exercise 2.1 in Hindi

Closure property, commutative of addition and multiplication and some examples of associative property of addition and multiplication are in Exercise 2.1 of Class 6 Maths. We will learn here the Identity for addition and multiplication also.

Chapter 3: Playing with Numbers

Class 6 Maths NCERT (https://ncert.nic.in/) Chapter 3 provides the practice of obtaining factors and multiplication of a number. In Class 6 Maths Chapter 3 Exercise 3.1 , there are lots of questions for finding factors or multiples.

Class 6 Maths Chapter 3 for CBSE and State Boards Class 6 Maths Exercise 3.1 Class 6 Maths Exercise 3.2 Class 6 Maths Exercise 3.3 Class 6 Maths Exercise 3.4 Class 6 Maths Exercise 3.5 Class 6 Maths Exercise 3.6 Class 6 Maths Exercise 3.7

Tiwari Academy is a popular online platform for NCERT solutions for all classes, including Class 6. It is considered to be one of the best platforms for Class 6 Maths solutions for several reasons. Exercise 3.2 of grade 6 Maths, describes Prime and Composite numbers as well as Even and Odd numbers. Test of divisibility by 2, 3, 5, 7, 9 and 11 are given in Exercise 3.3 of Class 6 Maths Solutions .

Class 6 Maths Chapter 3 in Hindi Medium Class 6 Maths Exercise 3.1 in Hindi Class 6 Maths Exercise 3.2 in Hindi Class 6 Maths Exercise 3.3 in Hindi Class 6 Maths Exercise 3.4 in Hindi Class 6 Maths Exercise 3.5 in Hindi Class 6 Maths Exercise 3.6 in Hindi Class 6 Maths Exercise 3.7 in Hindi

In Class 6 Exercise 3.4 , students get the idea of finding common factors and multiples of given integers. In Exercise 3.5 , the questions based on prime factorisation are given. 6th Maths Exercise 3.6 is based on HCF (Highest Common Factor), and Exercise 3.7 is designed for LCM (Least Common Multiple).

Chapter 4: Basic Geometrical Ideas

NCERT Textbook Class 6 Maths Chapter 4 starts with the concept of a Point, Line Segment, a Line, a Ray, Intersecting and Parallel line. Tiwari Academy’s NCERT solutions are written by experienced subject matter experts and cover all of the important topics in the textbook. The solutions are accurate and easy to understand.

Class 6 Maths Chapter 4 for CBSE Board Class 6 Maths Exercise 4.1 Class 6 Maths Exercise 4.2 Class 6 Maths Exercise 4.3

Class 6 Maths Chapter 4 for State Boards Class 6 Maths Chapter 4 Exercise 4.1 Class 6 Maths Chapter 4 Exercise 4.2 Class 6 Maths Chapter 4 Exercise 4.3 Class 6 Maths Chapter 4 Exercise 4.4 Class 6 Maths Chapter 4 Exercise 4.5 Class 6 Maths Chapter 4 Exercise 4.6

Tiwari Academy’s NCERT solutions are available for free online. This makes them accessible to all students, regardless of their financial background. In addition to these general benefits, Tiwari Academy’s NCERT solutions for Class 6 Maths can also help students to improve their conceptual understanding of the subjects.

Class 6 Maths Chapter 4 in Hindi Medium Class 6 Maths Exercise 4.1 in Hindi Class 6 Maths Exercise 4.2 in Hindi Class 6 Maths Exercise 4.3 in Hindi

All the questions of Exercise 4.1 of Class 6 Maths are based on facts as mentioned above. In the next section, Exercise 4.2 , we will deal with Simple Curves (Open and Closed Curves), Polygons, Sides, Vertices and Diagonals of a Polygon. Exercise 4.3 is based on Angles and its components.

Chapter 5: Understanding Elementary Shapes

The contents of Class 6 Maths Chapter 5 describes the measuring Line Segments using Ruler and Divider. In Exercise 5.1 , we have to measure the given line segments.

Class 6 Maths Chapter 5 for CBSE Board Class 6 Maths Exercise 5.1 Class 6 Maths Exercise 5.2 Class 6 Maths Exercise 5.3 Class 6 Maths Exercise 5.4 Class 6 Maths Exercise 5.5 Class 6 Maths Exercise 5.6 Class 6 Maths Exercise 5.7 Class 6 Maths Exercise 5.8

Class 6 Maths Chapter 5 for State Boards Class 6 Maths Chapter 5 Exercise 5.1 Class 6 Maths Chapter 5 Exercise 5.2 Class 6 Maths Chapter 5 Exercise 5.3 Class 6 Maths Chapter 5 Exercise 5.4 Class 6 Maths Chapter 5 Exercise 5.5 Class 6 Maths Chapter 5 Exercise 5.6 Class 6 Maths Chapter 5 Exercise 5.7 Class 6 Maths Chapter 5 Exercise 5.8 Class 6 Maths Chapter 5 Exercise 5.9

Tiwari Academy’s NCERT solutions provide step-by-step solutions to all of the problems in the textbook. These NCERT solutions are aligned with the CBSE syllabus. This means that by studying the Tiwari Academy NCERT solutions, students can be sure that they are covering all of the important topics that will be on their exams.

Class 6 Maths Chapter 5 in Hindi Medium Class 6 Maths Exercise 5.1 in Hindi Class 6 Maths Exercise 5.2 in Hindi Class 6 Maths Exercise 5.3 in Hindi Class 6 Maths Exercise 5.4 in Hindi Class 6 Maths Exercise 5.5 in Hindi Class 6 Maths Exercise 5.6 in Hindi Class 6 Maths Exercise 5.7 in Hindi Class 6 Maths Exercise 5.8 in Hindi

In Exercise 5.2 of grade VI math, students will observe and identify the angles like Right angle, Straight angle or Complete angle. Later on in Exercise 5.3 of 6th Maths, Acute angle, Obtuse angle, and Reflex angles to be discussed. Measuring the angles in Degree, using Protector is done in Exercise 5.4 of Class 6. We will learn the concepts of perpendicular lines or perpendicular bisectors in Exercise 5.5 of Class 6 Mathematics. Similarly, the classification of various triangles is given in Ex. 5.6 and that of quadrilaterals in Ex. 5.7 of Class 6 Maths. The identification, name and other properties of 3 – D figure is in the next exercises.

Chapter 6: Integers

NCERT Textbook Class 6 Maths Chapter 6 focusses on Integers. The main focus is on Integers on Number Line and Ordering of Integers using signs. Exercise 6.1 includes the basic question based on properties of Integers.

Class 6 Maths Chapter 6 for CBSE and State Boards Class 6 Maths Exercise 6.1 Class 6 Maths Exercise 6.2 Class 6 Maths Exercise 6.3

Tiwari Academy’s NCERT solutions are available in both English and Hindi. The solutions explain the concepts in the textbook in a clear and concise manner. This helps students to develop a deep understanding of the subjects, which is essential for success in their exams.

Class 6 Maths Chapter 6 in Hindi Medium Class 6 Maths Exercise 6.1 in Hindi Class 6 Maths Exercise 6.2 in Hindi Class 6 Maths Exercise 6.3 in Hindi

Class 6 Maths Solutions Exercise 6.2 focuses on the addition of Integers on Number Line. Succeeding in the same manner, Exercise 6.3 has a main focus on subtraction of Integers on Number Line.

Chapter 7: Fractions

Here, the class 6 Maths chapter 7 Exercise 7.1 describes the Fractions through pictorial representation and some other basic word problems.

Class 6 Maths Chapter 7 for CBSE and State Boards Class 6 Maths Exercise 7.1 Class 6 Maths Exercise 7.2 Class 6 Maths Exercise 7.3 Class 6 Maths Exercise 7.4 Class 6 Maths Exercise 7.5 Class 6 Maths Exercise 7.6

Here are some additional tips that may be helpful for students using Tiwari Academy’s NCERT solutions for Class 6 Maths. The Tiwari Academy NCERT solutions are designed to help students to answer the types of questions that are likely to be asked in their exams. It helps to improve their performance in their exams.

Class 6 Maths Chapter 7 in Hindi Medium Class 6 Maths Exercise 7.1 in Hindi Class 6 Maths Exercise 7.2 in Hindi Class 6 Maths Exercise 7.3 in Hindi Class 6 Maths Exercise 7.4 in Hindi Class 6 Maths Exercise 7.5 in Hindi Class 6 Maths Exercise 7.6 in Hindi

Class 6 Maths Exercise 7.2 deals with Proper Fraction, Improper Fraction, Mixed Fraction and Fraction on Number Line. Equivalent Fractions, the simple form of a Fraction removing common factors from Numerator and Denominator are the main points in Exercise 7.3 of Maths for Class 6. Students will be more aware about Like and Unlike Fractions and Comparison of two or more Fractions in Exercise 7.4 of 6th Mathematics. Addition and Subtraction of Fractions are the main practice in Exercise 7.5 as well as Exercise 7.6 of Class 6 Maths.

Chapter 8: Decimals

The Class 6 Maths Chapter 8 explains the Decimal numbers like Tenths, Hundredths and its representation on Number Line.

Class 6 Maths Chapter 8 in English Medium Class 6 Maths Exercise 8.1 Class 6 Maths Exercise 8.2 Class 6 Maths Exercise 8.3 Class 6 Maths Exercise 8.4

Many competitive exams, such as JEE Mains and NEET, are based on the NCERT syllabus. By studying the Tiwari Academy NCERT solutions, students can prepare for these exams more effectively. Overall, Tiwari Academy is a great resource for students who want to excel in their studies and to prepare for success in their future.

Class 6 Maths Chapter 8 in Hindi Medium Class 6 Maths Exercise 8.1 in Hindi Class 6 Maths Exercise 8.2 in Hindi Class 6 Maths Exercise 8.3 in Hindi Class 6 Maths Exercise 8.4 in Hindi

Conversion of Fraction as Decimals is the main topic to be discussed in Exercise 8.1 of Class 6 Maths. Terms related to Hundredths and Thousandths are given in Exercise 8.2 and the comparison of decimals in Exercise 8.3 of 6th Grade Maths. The application of Decimals representing Money, Weight, Length, etc., are given in Exercise 8.4 of Chapter 8, grade 6 Mathematics.

Chapter 9: Data Handling

The Class 6 Maths Chapter 9 Data Handling Exercise 9.1 describes about Pictographs using Tally Marks, whereas Exercise 9.2 explains how to draw a Pictograph.

Class 6 Maths Chapter 9 for CBSE Board Class 6 Maths Exercise 9.1

Class 6 Maths Chapter 9 for State Boards Class 6 Maths Chapter 9 Exercise 9.1 Class 6 Maths Chapter 9 Exercise 9.2 Class 6 Maths Chapter 9 Exercise 9.3 Class 6 Maths Chapter 9 Exercise 9.4

Class 6 Maths Chapter 9 in Hindi Medium Class 6 Maths Exercise 9.1 in Hindi

Data Handling is one of the core concepts in Statistics, which is one of the important topics to score well in all the classes.

Chapter 10: Mensuration

Class 6 Maths NCERT Book Chapter 10 Mensuration understands based concepts. Class 6 Maths Chapter 10 is a common concept for all the next classes.

Class 6 Maths Chapter 10 for CBSE and State Boards Class 6 Maths Exercise 10.1 Class 6 Maths Exercise 10.2 Class 6 Maths Exercise 10.3

Class 6 Maths Chapter 10 in Hindi Medium Class 6 Maths Exercise 10.1 in Hindi Class 6 Maths Exercise 10.2 in Hindi Class 6 Maths Exercise 10.3 in Hindi

Students need to practice this chapter properly, so that they will never face any problem to understand the questions related to Mensuration in future. Class 6 Maths NCERT Solutions Chapter 10 Exercise 10.1 is based on the perimeter of plane figures, whereas Exercise 10.2 is focusing on Areas of Plane figures. In Exercise 10.3 , we can find the areas of plane figures using a suitable formula.

Chapter 11: Algebra

The Class 6 Maths Chapter 11 deals with topic Algebra which is one of the three branches of Mathematics Geometry, Arithmetic and Algebra. Don’t be afraid to ask for help. If you are having difficulty understanding a concept or solving a problem, ask your teacher or a friend for help.

Class 6 Maths Chapter 11 for CBSE Board Class 6 Maths Exercise 11.1

Class 6 Maths Chapter 11 for State Boards Class 6 Maths Chapter 11 Exercise 11.1 Class 6 Maths Chapter 11 Exercise 11.2 Class 6 Maths Chapter 11 Exercise 11.3 Class 6 Maths Chapter 11 Exercise 11.4 Class 6 Maths Chapter 11 Exercise 11.5

Class 6 Maths Chapter 11 in Hindi Medium Class 6 Maths Exercise 11.1 in Hindi

Exercise 11.1 illustrates the concepts of Algebra using Matchsticks as well as using some word problems. Use the solutions in conjunction with your textbook and other resources. The solutions should not be used as a substitute for studying the textbook. Instead, they should be used to check your understanding of the concepts and to solve problems.

Chapter 12: Ratio and Proportion

The Class 6 Maths Chapter 12 Exercise 12.1 provides a good practice of Ratios. Most questions are related to daily life only.

Class 6 Maths Chapter 12 in English Medium Class 6 Maths Exercise 12.1 Class 6 Maths Exercise 12.2 Class 6 Maths Exercise 12.3

Use Tiwari Academy’s Class 6 Maths Solutions and Practice regularly. Try to solve some problems from the textbook or from the Tiwari Academy NCERT solutions every day. Don’t give up. If you keep practicing and don’t give up, you will eventually succeed.

Class 6 Maths Chapter 12 in Hindi Medium Class 6 Maths Exercise 12.1 in Hindi Class 6 Maths Exercise 12.2 in Hindi Class 6 Maths Exercise 12.3 in Hindi

In Exercise 12.2 , Ratios extent to Proportions. Now using two Ratios, we deal with the concept of Proportions. Unitary Methods play a key role in the mathematical calculation and these are useful for day to day life calculations. Exercise 12.3 of Class 6 Maths explains Unitary Method in a better way to understand.

Chapter 13: Symmetry

Find thorough NCERT solutions for Class 6 Maths Chapter 13, Symmetry. Expertly crafted explanations suitable for CBSE and state boards at Tiwari Academy. Class 6 Maths Chapter 13 Solutions for State Boards Class 6 Maths Chapter 13 Exercise 13.1 Class 6 Maths Chapter 13 Exercise 13.2 Class 6 Maths Chapter 13 Exercise 13.3

Chapter 14: Practical Geometry

Access comprehensive NCERT solutions for Class 6 Maths Chapter 14 on Practical Geometry. Detailed guides in clear language for CBSE and state board students at Tiwari Academy. Class 6 Maths Chapter 14 Solutions for State Boards Class 6 Maths Chapter 14 Exercise 14.1 Class 6 Maths Chapter 14 Exercise 14.2 Class 6 Maths Chapter 14 Exercise 14.3 Class 6 Maths Chapter 14 Exercise 14.4 Class 6 Maths Chapter 14 Exercise 14.5 Class 6 Maths Chapter 14 Exercise 14.6

Every student learns in a different way. Students who need extra support require individual attention in NCERT Class 6 Maths Solutions . Students provide individual guidance to each other, clarify doubts, and provide additional training or other clarification as needed. Add games, puzzles, and group activities to make learning math fun. Use math stories, songs or mnemonics to help you remember ideas.

The pace at which the curriculum is covered can vary from school to school and from one education system to another. Some schools or students may cover the curriculum faster or slower than others. The effectiveness of teaching and the quality of instructional materials can influence how quickly students grasp mathematical concepts. Well-designed lessons and engaging teaching methods can expedite the learning process. Students have different learning styles and aptitudes for mathematics. Some students may find certain concepts easier to grasp, while others may require more time and support.

Tiwari Academy’s best NCERT Solutions for Class 6 Maths helps to create a positive and encouraging learning. Remember that mastering math takes patience, practice, and a variety of study methods. By implementing these strategies and adapting them to the specific needs of your students, you can help them develop a strong foundation in math and build confidence in their abilities.

Some students may receive additional support, such as tutoring or extra classes, to help them master the curriculum. Adequate time should also be allocated for reviewing and practicing concepts, as this is essential for a thorough understanding of mathematics. In most cases, a standard class 6 mathematics curriculum is designed to be completed within the academic year, but it’s important to note that the pace at which students learn can vary. Some students may finish the course earlier, while others may need extra time.

If you’re studying class 6 mathematics outside of a traditional school setting or have unique circumstances, it’s important to set a reasonable study schedule and pace that suits your individual needs and goals. Consistency in studying, regular practice, and seeking help when needed can all contribute to successful completion of the course.

Use Class 6 Maths NCERT Solution with the help of many math-friendly games, apps, and websites available. If there’s a difficult question or chapter, break it down into smaller, manageable steps. Read step by step, making sure students understand each section before moving on to the next. This gentle approach helps build confidence and awareness.

How to learn Class 6 Maths using NCERT Solutions?

According to academic session 2024-25, there are only 12 chapters in class 6 mathematics syllabus. Scoring well in Class 6 math using NCERT solutions requires a systematic approach and regular practice. As you prepare for exams, NCERT solutions are an excellent tool for revision. You can review key concepts, solve additional practice problems, and verify your solutions using these resources. Follow the videos and PDF solutions of class 8 Maths to get good marks in exams. Follow the steps to help you achieve this.

Step 1: Understand the 6th Maths NCERT Textbook and create a Study Schedule.

Step 2: practice regularly using revised ncert book for class 6 and take notes., step 3: solve class 6 maths previous year question papers and work on weak areas., step 4: take help from online educational websites like tiwari academy for revision., step 5: test yourself doing regular practice of previous chapters..

Regular practice is essential to strengthen math skills. A variety of Class 6 Maths NCERT Solutions PDF with practice tasks and worksheets are available on Tiwari Academy for Class 6 students. Students should practice regularly at home and also encourage their classmates to practice.

How to score well in Class 6 Maths terminal Exams?

If a student of class VI wants to get more than 90% in Maths marks, he/she must first complete NCERT. Do all the examples and questions given in the exercise. After going through the NCERT Textbook for Class VI Maths, start working on the NCERT Exemplar and Sample Paper Book now. These have questions that raise the level of mind to think about mathematical concepts more than ever before. Regular practice of both these books helps the students to score more than 90% marks in class 6 Maths. To know more steps about to scoring well in 6th Maths, please follow the link .

What are the difficult Chapters for Class 6 Maths?

According to new syllabus, there are total 12 chapters in class 6 Maths. Of these, Chapter 10 Measurement based chapter Mensuration and Chapter 12 Ratios and Proportion also require more time to understand and practice. There are many questions which need to be practiced two or three times to understand them properly. Hence, these two chapters are considered as the tough chapters of the NCERT Book for Class 6 Maths book.

How to practice Class 6 Maths to get good marks?

Most of the questions asked in exams are picked up from NCERT Textbooks only. If a student spend at least one hour time to practice Class 6 Maths Solutions and NCERT books, he can easily score more than passing marks. Examples, given just before each exercises, are also important for the examination point of view. These examples are also helpful during the exercise practice to understand the way of solving different questions.

Which chapters of Class 6 Maths are easy to score well?

As per the rationalised syllabus and new NCERT book released, the 6th Maths book contains only 12 chapters. Chapter 1, 2, 3, 5 and 9 are easier to practice and score good marks in exams. These are not only easy chapters but interesting also. These chapters require less time to practice but good to score marks in exams. During the exams, students should solve the questions of these chapter first then go for the difficult chapters.

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Providing help in science for class 6 to 10. Adviser in Tiwari Academy for the science related subjects subject as well as videos contents. Ample teaching experience in schools. I am not only working for Tiwari Academy but also provide new ideas for the website and apps.

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NCERT Solutions

• NCERT Class 6
• NCERT 6 Maths
• Chapter 3: Playing With Numbers
• Exercise 3.2

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.2

The NCERT Solutions For Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.2 is the continuation of the 1st exercise of the chapter.  In the previous exercise, we have learnt about the factors and multiples. Now, in this exercise of  NCERT Class 6 Maths Chapter 3, we get a brief idea about the prime and composite numbers. We, at BYJU’S, have provided NCERT Solutions for the students to aid them in understanding the steps involved in solving the problems. The numbers which have factors as 1 and the number itself are prime numbers and those having many factors are composite numbers. Learn more about prime and composite numbers by practising the  NCERT Solutions of Class 6 Maths  that is being provided here for the second exercise of Chapter 3 Playing with Numbers.

• Chapter 1 Knowing our Numbers
• Chapter 2 Whole Numbers
• Chapter 3 Playing With Numbers
• Chapter 4 Basic Geometrical Ideas
• Chapter 5 Understanding Elementary Shapes
• Chapter 6 Integers
• Chapter 7 Fractions
• Chapter 8 Decimals
• Chapter 9 Data Handling
• Chapter 10 Mensuration
• Chapter 11 Algebra
• Chapter 12 Ratio And Proportion
• Chapter 13 Introduction To Symmetry
• Chapter 14 Practical Geometry
• Exercise 3.1 Chapter 3 Playing With Numbers
• Exercise 3.2 Chapter 3 Playing With Numbers
• Exercise 3.3 Chapter 3 Playing With Numbers
• Exercise 3.4 Chapter 3 Playing With Numbers
• Exercise 3.5 Chapter 3 Playing With Numbers
• Exercise 3.6 Chapter 3 Playing With Numbers
• Exercise 3.7 Chapter 3 Playing With Numbers

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.2

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Access NCERT Solutions for Class 6 Chapter 3: Playing with Numbers Exercise 3.2

1. What is the sum of any two (a) Odd numbers? (b) Even numbers?

(a) The sum of any two odd numbers is an even number.

Examples: 5 + 3 = 8

15 + 13 = 28

(b) The sum of any two even numbers is an even number.

Examples: 2 + 8 = 10

12 + 28 = 40

2. State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(c) The product of three odd numbers is odd.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

(a) False. The sum of three odd numbers is odd.

Example: 7 + 9 + 5 = 21 i.e., odd number

(b) True. The sum of two odd numbers and one even number is even.

Example: 3 + 5 + 8 = 16 i.e is even number.

(c) True. The product of three odd numbers is odd.

Example: 3 × 7 × 9 = 189 i.e., is an odd number.

(d) False. If an even number is divided by 2, the quotient is even.

Example: 8 ÷ 2 = 4

(e) False, All prime numbers are not odd.

Example: 2 is a prime number but it is also an even number.

(f) False. Since, 1 and the number itself are factors of the number

(g) False. Sum of two prime numbers may also be an odd number

Example: 2 + 5 = 7 i.e., odd number.

(h) True. 2 is the only even prime number.

(i) False. Since, 2 is a prime number.

(j) True. The product of two even numbers is always even.

Example: 2 × 4 = 8 i.e., even number.

3. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.

The prime numbers with same digits upto 100 are as follows:

4. Write down separately the prime and composite numbers less than 20.

2, 3, 5, 7, 11, 13, 17 and 19 are the prime numbers less than 20

4, 6, 8, 9, 10, 12, 14, 15, 16 and 18 are the composite numbers less than 20

5. What is the greatest prime number between 1 and 10?

2, 3, 5 and 7 are the prime numbers between 1 and 10. 7 is the greatest prime number among them.

6. Express the following as the sum of two odd primes.

(a) 3 + 41 = 44

(b) 5 + 31 = 36

(c) 5 + 19 = 24

(d) 5 + 13 = 18

7. Give three pairs of prime numbers whose difference is 2. [Remark: Two prime numbers whose difference is 2 are called twin primes].

The three pairs of prime numbers whose difference is 2 are

8. Which of the following numbers are prime?

1 × 23 = 23

23 × 1 = 23

Therefore, 23 has only two factors 1 and 23. Hence, it is a prime number.

1 × 51 = 51

3 × 17 = 51

Therefore, 51 has four factors 1, 3, 17 and 51. Hence, it is not a prime number, it is a composite number.

1 × 37 = 37

37 × 1 = 37

Therefore, 37 has two factors 1 and 37. Hence, it is a prime number.

1 × 26 = 26

2 × 13 = 26

Therefore, 26 has four factors 1, 2, 13 and 26. Hence, it is not a prime number, it is a composite number.

9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Seven composite numbers between 89 and 97 both which are prime numbers are 90, 91, 92, 93, 94, 95 and 96

Numbers                                                                                                  Factors

90                                                                                       1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

91                                                                                        1, 7, 13, 91

92                                                                                       1, 2, 4, 23, 46, 92

93                                                                                       1, 3, 31, 93

94                                                                                       1, 2, 47, 94

95                                                                                       1, 5, 19, 95

96                                                                                       1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

10. Express each of the following numbers as the sum of three odd primes:

(a) 3 + 5 + 13 = 21

(b) 3 + 5 + 23 = 31

(c) 13 + 17 + 23= 53

(d) 7 + 13 + 41 = 61

11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint: 3 + 7 = 10)

The five pairs of prime numbers less than 20 whose sum is divisible by 5 are

2 + 13 = 15

3 + 17 = 20

7 + 13 = 20

19 + 11 = 30

12. Fill in the blanks:

(a) A number which has only two factors is called a ______.

(b) A number which has more than two factors is called a ______.

(c) 1 is neither ______ nor ______.

(d) The smallest prime number is ______.

(e) The smallest composite number is _____.

(f) The smallest even number is ______.

(a) A number which has only two factors is called a prime number.

(b) A number which has more than two factors is called a composite number.

(c) 1 is neither a prime number nor a composite number.

(d) The smallest prime number is 2

(e) The smallest composite number is 4

(f) The smallest even number is 2.

Also, explore – 

NCERT Solutions for Class 6 Maths Chapter 3

NCERT Solutions for Class 6

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Class 6 Mathematics Assignments

We have provided below free printable Class 6 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 6 Mathematics . These Assignments for Grade 6 Mathematics cover all important topics which can come in your standard 6 tests and examinations. Free printable Assignments for CBSE Class 6 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 6 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 6 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 6. Students can click on the links below and download all Pdf Assignments for Mathematics class 6 for free. All latest Kendriya Vidyalaya Class 6 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 6 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 6 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 6th. Our expert faculty have covered Class 6 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 6 Mathematics and CBSE Assignments for Mathematics Class 6 will be really helpful for standard 6th students to prepare for the class tests and school examinations. Class 6th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 6 Mathematics Download in Pdf

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Advantages of Class 6 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 6, you will be able to easily get full list of solved important questions which can come in your examinations.
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• Class 6 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 6 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 6 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 6 which you can download in Pdf

We provide here Standard 6 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 6, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 6 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 6 for all subjects. You can download them all and use them offline without the internet.

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NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Maths is a very important resource for students of Class 6. CBSE 6th class maths textbook solutions includes answers of all questions except the ones which are not in the syllabus anymore. NCERT class 6 maths solutions have been provided by the most experienced teachers. A very simple approach has been followed while solving the questions and designing the class 6 maths NCERT solutions. Students will find it extremely easy to understand the problems and how to go about solving them. You can also practice  Extra Questions for Class 6 Maths  on LearnCBSE.in

NCERT Solutions for Class 6 Maths are given below for all chapters.

• Chapter 1 Knowing Our Numbers
• Chapter 2 Whole Numbers
• Chapter 3 Playing With Numbers
• Chapter 4 Basic Geometrical Ideas
• Chapter 5 Understanding Elementary Shape
• Chapter 6 Integers
• Chapter 7 Fractions
• Chapter 8 Decimals
• Chapter 9 Data Handling
• Chapter 10 Mensuration
• Chapter 11 Algebra
• Chapter 12 Ratio and Proportion
• Chapter 13 Symmetry
• Chapter 14 Practical Geometry

Click on the name of the chapter for which you want to check the solutions and you will be directed to the page for that chapter. You can then go through the detailed, step-wise CBSE 6th class maths questions and answers for each and every question for that chapter.

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers

• Class 6 Maths Knowing our Numbers Exercise 1.1
• Class 6 Maths Knowing our Numbers Exercise 1.2
• Class 6 Maths Knowing our Numbers Exercise 1.3
• Knowing Our Numbers Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers

• Class 6 Maths Whole Numbers Exercise 2.1
• Class 6 Maths Whole Numbers Exercise 2.2
• Class 6 Maths Whole Numbers Exercise 2.3
• Whole Numbers Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers

• Playing with Numbers Class 6 Ex 3.1
• Playing with Numbers Class 6 Ex 3.2
• Playing with Numbers Class 6 Ex 3.3
• Playing with Numbers Class 6 Ex 3.4
• Playing with Numbers Class 6 Ex 3.5
• Playing with Numbers Class 6 Ex 3.6
• Playing with Numbers Class 6 Ex 3.7
• Playing with Numbers Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

• Class 6 Maths Basic Geometrical Ideas Exercise 4.1
• Class 6 Maths Basic Geometrical Ideas Exercise 4.2
• Class 6 Maths Basic Geometrical Ideas Exercise 4.3
• Class 6 Maths Basic Geometrical Ideas Exercise 4.4
• Class 6 Maths Basic Geometrical Ideas Exercise 4.5
• Class 6 Maths Basic Geometrical Ideas Exercise 4.6
• Basic Geometrical Ideas Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shape

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9
• Understanding Elementary Shapes Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 6 Integers

• Integers Class 6 Ex 6.1
• Integers Class 6 Ex 6.2
• Integers Class 6 Ex 6.3
• Integers Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 7 Fractions

• Fractions Class 6 Ex 7.1
• Fractions Class 6 Ex 7.2
• Fractions Class 6 Ex 7.3
• Fractions Class 6 Ex 7.4
• Fractions Class 6 Ex 7.5
• Fractions Class 6 Ex 7.6
• Fractions Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 8 Decimals

• Class 6 Maths Decimals Exercise 8.1
• Class 6 Maths Decimals Exercise 8.2
• Class 6 Maths Decimals Exercise 8.3
• Class 6 Maths Decimals Exercise 8.4
• Class 6 Maths Decimals Exercise 8.5
• Class 6 Maths Decimals Exercise 8.6
• Decimals Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 9 Data Handling

• Class 6 Maths Data Handling Exercise 9.1
• Class 6 Maths Data Handling Exercise 9.2
• Class 6 Maths Data Handling Exercise 9.3
• Class 6 Maths Data Handling Exercise 9.4
• Data Handling Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 10 Mensuration

• Class 6 Maths Mensuration Exercise 10.1
• Class 6 Maths Mensuration Exercise 10.2
• Class 6 Maths Mensuration Exercise 10.3
• Mensuration Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 11 Algebra

• Class 6 Maths Algebra Exercise 11.1
• Class 6 Maths Algebra Exercise 11.2
• Class 6 Maths Algebra Exercise 11.3
• Class 6 Maths Algebra Exercise 11.4
• Class 6 Maths Algebra Exercise 11.5
• Algebra Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 12 Ratio and Proportion

• Class 6 Maths Ratio and Proportion Exercise 12.1
• Class 6 Maths Ratio and Proportion Exercise 12.2
• Class 6 Maths Ratio and Proportion Exercise 12.3
• Ratio and Proportion Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 13 Symmetry

• Class 6 Maths Symmetry Exercise 13.1
• Class 6 Maths Symmetry Exercise 13.2
• Class 6 Maths Symmetry Exercise 13.3
• Symmetry Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 14 Practical Geometry

• Class 6 Maths Practical Geometry Exercise 14.1
• Class 6 Maths Practical Geometry Exercise 14.2
• Class 6 Maths Practical Geometry Exercise 14.3
• Class 6 Maths Practical Geometry Exercise 14.4
• Class 6 Maths Practical Geometry Exercise 14.5
• Class 6 Maths Practical Geometry Exercise 14.6
• Practical Geometry Class 6 Extra Questions

Maths Formulas for Class 6 RD Sharma Class 6 Solutions Maths NCERT Solutions

Mathematics is an interesting subject. Unfortunately, many students find it difficult. But that’s not because Mathematics is really a difficult subject. Students find it difficult because most of them do not have their basics clear for the subject. Lack of sufficient practice tool is a reason why solving Mathematical problems seems a tough nut to crack.

Unlike other subjects, rote learning cannot help you to excel this subject. Even for other subjects, rote learning is not recommended as it won’t be of much use after a point of time. And Mathematics, from the very beginning, needs one to think logically. But just because the subject needs logical thinking and analytical skills does not mean it is tough. Mathematics needs practice and with practice, anything can be perfected, even the way you think and analyze. So, it is of utmost importance to take Mathematics seriously right from your early school life. Getting your basics clear at this point will make it easier for you to handle difficult concepts as you grow older.

Mathematics of Class 6, 7 and 8 standard play a vital role in strengthening the fundamentals of the subject. It is at this point, Mathematics goes beyond simple addition, subtraction, multiplication, and division and move onto more complex concepts. So, one must prepare for this subject in a serious manner and get all their doubts clear. Otherwise, they won’t be able to cope with the subject later, especially if they are planning to take up Science in their Higher Secondary level.

Class 6 Maths Chapter 1 Knowing Our Numbers

• Introduction
• Comparing Numbers Worksheet
• Large Numbers In Practice
• Using Brackets
• Roman Numerals Chart

Class 6 Maths Chapter 2 Whole Numbers

• Whole Numbers
• The Number Line
• Properties of Whole Numbers
• Patterns In Whole Numbers

Class 6 Maths Chapter 3 Playing With Numbers

• Factors And Multiples Worksheet
• Prime And Composite Numbers Chart and Worksheets
• Divisibility Rules 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,2
• Common Factors And Common Multiples
• Some More Divisibility Rules
• Prime Factorisation Worksheets
• Highest Common Factor Worksheets
• Lowest Common Multiple Worksheet
• Hcf And Lcm Formulas, Problems with Solutions

Class 6 Maths Chapter 4 Basic Geometrical Ideas

• Points, A Line Segment, Ray, and A Line
• Intersecting Lines and Parallel Lines
• Types of Polygons
• What is Angle in Geometry
• Median, altitude of Triangle
• What is a Quadrilateral
• Parts of the Circle

Class 6 Maths Chapter 5 Understanding Elementary Shapes

• Comparison of Line Segments
• Different Types of Angles
• Measure an Angle with a Protractor
• Classification of Triangles
• Different Types of Quadrilaterals
• Different types of Three Dimensional Shapes

Class 6 Maths Chapter 6 Integers

• Integers Examples
• Operations with Integers Worksheet

Class 6 Maths Chapter 7 Fractions

• Types of fraction
• Fraction on The Number Line
• Proper Fractions
• Improper And Mixed Fractions
• Equivalent Fractions Chart
• Simplest Form Of A Fraction
• Like Fractions
• Comparing Fractions Worksheets
• Addition And Subtraction Of Fractions

Class 6 Maths Chapter 8 Decimals

• Tenths and Hundreths
• Convert Unlike Decimals to like decimals
• Using Decimals
• Addition Of Numbers With Decimals
• Subtraction Of Decimals

Class 6 Maths Chapter 9 Data Handling

• Recording Data
• Collection and Organisation of Data
• Pictograph Examples and Worksheets
• Interpretation of A Pictograph
• Drawing A Pictograph
• A Bar Graph

Class 6 Maths Chapter 10 Mensuration

• Perimeter of Closed Shapes
• Find Area of Plane Figures

Class 6 Maths Chapter 11 Algebra

• Matchstick Patterns
• The Idea Of A Variable
• More Matchstick Patterns
• More Examples Of Variables
• Use Of Variables In Common Rules
• Expressions With Variables
• Using Expressions Practically
• What Is An Equation?
• Solution Of An Equation

Class 6 Maths Chapter 12 Ratio and Proportion

• What is Ratio and Proportion
• Unitary Method

Class 6 Maths Chapter 13 Ratio and Proportion

• Making Symmetric Figures: Ink-blot Devils
• Figures with Two Lines of Symmetry
• Figures with Multiple (more than two) Lines of Symmetry
• Reflection and Symmetry

Class 6 Maths Chapter 14 Practical Geometry

• Construction of a Circle
• Construction of a Line Segment
• Construction of a Perpendicular Bisector
• Construction of Angles using compass ruler

NCERT Solutions For Class 6 Maths Solutions (Download PDF)

Clear your doubt then and there. This will help you not only to secure good marks in your Class 6 final exams, but also in other competitive exams that are conducted for students of Class 6. As you go to higher classes, it will help you to crack competitive scholarship exams, like NTSE, as well. So, make the best use of these solutions.

Remember, at this point, you cannot afford to skip any chapter even if it is not so important from the exam point of view. At this point, all the chapters are equally important so that your command over the subject gets really good. So, as you solve questions from your NCERT Maths textbook, go through the NCERT Solutions for Class 6 Maths here every time you face any difficulty with any question. Do not skip it for later.

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Assignments For Class 6 Mathematics

Assignments for Class 6 Mathematics have been developed for Standard 6 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 6 Mathematics from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 6 Mathematics. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics book and get good marks in class 6 exams.

Assignments for Class 6 Mathematics as per CBSE and NCERT pattern

More Assignments for Class 6 Mathematics

Assignments for Class 6 Mathematics as per CBSE NCERT pattern

All students studying in Grade 6 Mathematics should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics exam for standard 6. We have made sure that all topics given in your textbook for Mathematics which is suggested in Class 6 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

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All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 6 Mathematics teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 6 Mathematics Assignments PDF.

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