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

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