NCERT Solutions For Class 6 Maths Chapter 3 Playing With Numbers are exercise wise solutions of the NCERT textbooks questions. The NCERT Solutions For Class 6 Maths Chapter 3 covers topics such as Simplification of brackets, Multiples and factors, Even/odd and prime/composite, Co-prime numbers, Testing divisibility, Common Factors and Common Multiples, More Divisibility Rules, Prime Factorization, HCF and LCM, Prime Factorization , Method for HCF and LCM, Property : LCM × HCF = product of two numbers. Thus, for students of class 6 we have provided NCERT Solutions for class 6 Maths Chapter 3 pdf to help them test their knowledge with the intext questions and solutions based on which they can access their knowledge and learn what they do not know as well.

This chapter 3 comprises of a wide range of topics. They are –

- Introduction
- Factors and Multiples
- Prime and Composite Numbers
- Tests for Divisibility of Numbers
- Divisibility by 10
- Divisibility by 5
- Divisibility by 2
- Divisibility by 3
- Divisibility by 6
- Divisibility by 4
- Divisibility by 8
- Divisibility by 9
- Divisibility by 11

- Common Factors and Common Multiples
- Some More Divisibility Rules
- Prime Factorisation
- Highest Common Factor
- Lowest Common Multiple
- Some Problems on HCF and LCM

### NCERT Solutions Class 6 Maths Chapter 3 Exercises

- NCERT Solutions For Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.1
- NCERT Solutions For Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.2

__Exercise 3.1__

*1. Find the sum of any two numbers ?*

*(a) odd numbers*

*(b) even numbers*

**SOLUTION (a) SOLUTION (b)**

e.g. 6 + 3 = 9 e.g. 12 + 14 = 26

*2. Write down the prime numbers less than 20.*

**SOLUTION:**

The numbers which are divisible by itself is known as prime numbers . prime numbers which are less than 20 are,

2 , 3 , 5 , 7 , 11 , 13 , 17 , 19.

*3. Write down the composite numbers less than 20.*

**SOLUTION:**

The numbers which are not prime numbers is known as composite numbers. The composite numbers which are less than 20 are,

4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 18 .

*4. The numbers 31 and 13 are prime numbers. Both these numbers have same digits 1 and 7. Find such pairs of prime numbers up to 100.*

**SOLUTION:**

(79 , 97) (37 , 73) (17 , 71)

**5. Express the following in the form of sum of two odd primes.**

SOLUTION :

(a) 24 = 5 + 19

(b) 44 = 7 + 37

(c) 18 = 7 + 11

(d) 36 = 31 + 5

*6. Find any three pair of prime numbers whose difference is two.*

**SOLUTION:**

Two prime numbers whose difference is ‘2’ is also called as twin primes or twin prime number.

3 pairs : (41 , 43) ( 73 , 71) (5 , 3)

*7. Express the following numbers in the form of sum of three odd primes.*

**SOLUTION:**

(a) 53 = 31 + 3 + 19

(b) 61 = 19 + 11 + 31

(c) 31 = 19 + 5 + 7

*8. Write down the 3 pairs of prime numbers which is less than 20 and also whose sum is divisible by 5.*

**SOLUTION:**

(*) 17 + 3 = 20 (5 x 4 = 20. It is divisible by 5)

(*) 13 + 2 = 15 (5 x 3 = 15. It is divisible by 5)

(*) 11 + 19 = 30 ( 5 x 6 = 30. It is divisible by 5)

*9. FILL IN THE BLANKS.*

(*) 1 is neither _____ nor ________. ans: (composite , prime)

(*) The number which has only one factor is called _________. ans: (prime number)

(*) The smallest composite number is ________. ans: ( 4 )

*10. TRUE OR FALSE.*

(*) The sum of two prime numbers is always even. Ans : false

e.g. 3 + 2 = 5 (i.e) odd

(*) The product of three odd numbers is odd. Ans : true

e.g. 5 x 7 x 3 = 105 (i.e) odd

(*) The product of two even numbers is always even. Ans : true

e.g 2 x 4 = 8 (i.e) even

6 x 2 = 12 (i.e) even

__Exercise 3.2__

*1. Find out the common factors of the following.*

*(a) 28 & 20*

*(b) 25 & 15*

*(c) 56 & 120*

**SOLUTION: **

(a) Factors of (20) = 1 , 10 , 20, 2 , 4 ,5

Factors of (28) = 7 , 14 , 28 ,1 , 2 , 4 ,

The factors that are common are : 4, 2, 1

(b) Factors of (15) = 1 , 15,3 , 5

Factors of (25) = 1 ,25,5

The factors that are common are : 1 , 5.

(c) Factors of (56) = 1 , 14 , 28 , 56 ,2 , 4 , 7 , 8.

Factors of (120) = 1 ,30 ,40 , 10 ,12 , 2 ,3 ,4 ,5 ,6 ,8 , 15 ,20 ,24 ,60 , 120.

The factors that are common are : 1 , 2 , 4 , 8 .

*2. Find the numbers (all) which are less than 100 and also common multiples of 4 & 3.*

**SOLUTION:**

(*) multiples of 3 = 3, 15, , 6, 9, 12

(*) multiples of 4 = 4 ,8, 12, 16, 20

The Common multiples are = 12, 36, 48,24, 60, 72, 84, 96.

*3. From the given numbers , find which numbers are co prime numbers ?*

*(a) 68 and 17*

*(b) 16 and 81*

*(c) 35 and 18*

**SOLUTION: **

(*) 68 and 17

Factors of 68 = 1, 2, 4, 17, 34, 68

Factors of 17 = 1, 17

The factors that are common are : 1 , 17

Since it has common factors other than 1, the above given 2 number is not a co prime.

(*) 16 and 81

Factors of 16 = 1, 2, 4, 8, 16

Factors of 81 = 1, 3, 9, 27, 81

The common factor is 1. Therefore the given two number is co prime.

(*) 35 and 18

Factors of 35 = 1, 5, 7, 35

Factors of 18 = 1, 2, 3, 6, 9, 18

Common factor is 1. Therefore the given two number is co prime.

*4. A particular number is divisible by both 14 and 5. Find the other number that is always divisible.*

**SOLUTION:**

Factors of 5 = 1 , 5

Factors of 14 = 1, 2, 7

The common factors of these numbers is 1. Therefore, the given two number is co prime number and also the number will be divisible by their product.

*5. A number is divisible by 12. Find the other numbers, which are divisible of 12.*

**SOLUTION:**

The factors are : 1, 2, 3, 4, 6 , 12

Therefore, the numbers 1,2,3,4,6 other than 12 by which this number is also divisible.

*6. Find the common factors of the following given below:*

(*) 4 , 8 and 12

(*) 5 , 15 , 25

**SOLUTION:**

(*) 4 , 8 and 12

Factors of 4 = 1 , 2 , 4

Factors of 8 = 1 , 2 , 4 , 8

Factors of 12 = 1 , 2 , 3 , 4 , 6 , 12

The common factors are : 1, 2, 4.

(*) 5 , 15 , 25

The factors of 5 = 1 , 5

The factors of 15 = 1 , 3 , 5 , 15

The factors of 25 = 1 , 5 , 25

The common factors are : 1 , 5

In NCERT solutions Class 6 Maths Chapter 3, the conclusion of the lesson is divided into 2 parts. They are – exercise and What have we discussed?. We at BYJU’S provide solutions for all the classes in a simple and and an easier way. BYJU’S provides solutions for all the classes and chapters in brief. For more NCERT solutions, study materials of all the subjects and of all the classes visit BYJU’S or download the app for more information and learning experience.