## NCERT solutions for class 6 Maths

## Chapter – 3

**Playing with Numbers**

**Exercise 3.4**

## Ex 3.4 Question 1.

**Find the common factors of:**

**(a) 20 and 28**

**(b) 15 and 25**

**(c) 35 and 50**

**(d) 56 and 120**

**Solution:**

(a) 20 and 28

Factors of 20 =1, 2, 4, 5, 10, 20

Factors of 28 = 1, 2, 4, 7, 28

Hence, the common factors =1, 2, and 4.

(b) 15 and 25

Factors of 15 =1, 3, 5, 15

Factors of 25 = 1, 5, 25

Hence, the common factors = 1 and 5.

(c) 35 and 50

Factors of 35 = 1, 5, 7, 35

Factors of 50 = 1, 2, 5, 10, 50

Hence, the common factors = 1 and 5.

(d) 56 and 120

Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

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

Hence, the common factors =1,2, 4, and 8.

## Ex 3.4 Question 2.

**Find the common factors of:**

**(a) 4, 8 and 12**

**(b) 5, 15 and 25**

**(6) 8 9484**

**Solution:**

(a) 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

Hence, the common factors = 1, 2, and 4.

(b) 5, 15 and 25

Factors of 5 = 1, 5

Factors of 15 = 1, 3, 5, 15

Factors of 25 = 1, 5, 25

Hence, the common factors = 1 and 5.

## Ex 3.4 Question 3.

**Find the first three multiples of:**

**(a) 6 and 8**

**(b) 12 and 18**

**Solution:**

(a) 6 and 8

Multiple of 6 = 6, 12, 18, 24, 30, 36 , 42 , 48 , 54 , 60 , 66 , 72…………….

Multiple of 8 = 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80………………………

First three common multiples of 6 and 8 = 24, 48, 72.

(b) 12 and 18.

Multiples of 12 =12 , 24 , 36 , 48 , 60 , 72 , 84 , 96 , 108 , 120……………………….

Multiples of 18 = 18 , 36 , 54 , 72 , 90 , 108…………………………….

First three common multiples of 12 and 18 = 36, 72, 108.

## Ex 3.4 Question 4.

**Write all the numbers less than 100 which are common multiples of 3 and 4.**

**Solution:**

Multiple of 3 =

Common multiples of 3 and 4 less than 100= 12, 24, 36, 48, 60, 72, 84, and 96.

## Ex 3.4 Question 5.

**Which of the following numbers are co-prime?**

**(a) 18 and 35**

**(b) 15 and 37**

**(c) 30 and 415**

**(d) 17 and 68**

**(e) 216 and 215**

**(f) 81 and 16**

**Solution:**

(a) 18 and 35

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

Factors of 35 = 1, 5, 7, 35

Common factors of 18 and 35 = 1.

Hence, 18 and 35 are co-prime.

(b) 15 and 37

Factors of 15= 1, 3, 5, 15

Factors of 37 = 1,37

The common factor of 15 and 37 = 1.

Hence, 15 and 37 are co-prime.

(c) 30 and 415

Factors of 30 = 1, 2, 3, 5, 6, 15, 30

Factors of 415 = 1, 5, 83

Common factors of 30 and 415 = 1 and 5

Hence, 30 and 415 are not co-prime.

(d) 17 and 68

Factors of 17 = 1, 17

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

Common factors of 17 and 68 = 1 and 17

Hence, 17 and 68 are not co-prime.

(e) 216 and 215

Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 54, 72, 108, 216

Factors of 215 = 1, 5, 43

Common factor of 216 and 215 = 1

Hence, 216 and 215 are co-prime.

(f) 81 and 16

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

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

Common to 81 and 16 = 1

Hence, 81 and 16 are co-prime.

## Ex 3.4 Question 6.

**A number is divisible by both 5 and 12. By which other will that number be always divisible?**

**Solution:**

5 x 12 = 60.

Hence, the number must be divisible by 60.

## Ex 3.4 Question 7.

**A number is divisible by 12. By what other will that number be divisible?**

**Solution:**

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

Hence the number also be divisible by= 1, 2, 3, 4, 6 and 12.