Chapter - 3 - EXERCISE 3.4 - Playing with Numbers (NCERT Class 6th Maths Solution)

1. Find the common factors of : 
(a) 20 and 28     (b) 15 and 25      (c) 35 and 50     (d) 56 and 120

Solution/Explanation:

(a) 20 and 28

Factors of 20=1,2,4,5,10,20 

Factors of 28=1,2,4,7,14,28 

Common factors =1,2,4 

 (b) 15 and 25

Factors of 15=1,3,5,15 

Factors of 25=1,5,25 

Common factors =1,5

(c) 35 and 50   

Factors of 35=1,5,7,35 

Factors of 50=1,2,5,10,25,50 

Common factors =1,5

(d) 56 and 120

Factors of 56=1,2,4,7,8,14,28,56 

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

 Common factors =1,2,4,8

2. Find the common factors of : 
(a) 4, 8 and 12            (b) 5, 15 and 25


Solution/Explanation:
(a) Factors of 4 = 1, 2, 4

Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Common factors of 4, 8 and 12 = 1, 2, 4

(b) Factors of 5 = 1, 5 Factors
of 15 = 1, 3, 5, 15 Factors
of 25 = 1, 5, 25
Common factors of 5, 15 and 25 = 1,5

3. Find first three common multiples of : 
(a) 6 and 8                     (b) 12 and 18

Solution/Explanation:

(a) 6 and 8

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

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

The first three common multiples of 6 and 8 are = 24, 48, 72

(b) 12 and 18

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

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

The first three common multiples of 12 and 18 are = 36, 72, 108

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

Solution/Explanation:

Multiple of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66,69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99


Multiple of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88,92,96,100
Common multiples of 3 and 4 = 12, 24, 36, 48, 60, 72, 84, 96

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/Explanation:
(a) 18 and 35 

Factors of 18=1,2,3,6,9,18

Factors of 35=1,5,7,35 

Common factor =1 

Therefore, the given two numbers are co-prime.  

(b)15 and 37 

Factors of 15=1,3,5,15 

Factors of 37=1,37 

Common factors =1 

Therefore, the given two numbers are co-prime. 

(c) 30 and 415

Factors of 30=1,2,3,5,6,10,15,30 

Factors of 415=1,5,83,415 

Common factors =1,5 

As these numbers have a common factor other than 1, the given two numbers are non co-prime.  

(d) 17 and 68

Factors of 17=1,17

 Factors of 68=1,2,4,17,34,68 

Common factors =1,17 

 As these numbers have a common factor other than 1, the given two numbers are non co-prime.  

(e) 216 and 215

 Factors of 216=1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

 Factors of 215=1,5,43,215 

Common factors =1

 Therefore, the given two numbers are co-prime.  

(f) 81 and 16

 Factors of 81=1,3,9,27,81 

Factors of 16=1,2,4,8,16 

Common factors =1

 Therefore, the given two numbers are co-prime

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

Solution/Explanation:

5 and 12 are co-primes and we know that if a number is divisible by two co-primes, then it is a known fact that it is also divisible by their product.
The product of 5 and 12 is 60. Hence, the number is always divisible by 60.

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

Solution/Explanation:

factor of 12 are 1,2,3,4,6,12

therefore, the number also divisible by 1,2,3,4 and 6