NCERT Solutions For Class 6 Maths Chapter 3

Playing With Numbers

NCERT Solutions For Class 6 Maths chapter 3 Exercise 3.4

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.5 Exercise 3.6 Exercise 3.7

Question 1

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

Answer 1

(a) 20 and 28
Factors of 20 =1, 2, 4, 5, 10, 20
Factors of 28 = 1, 2, 4, 7, 28
The common factors are 1, 2 and 4.
(b) 15 and 25
Factors of 15 = 1, 3, 5, 15
Factors of 25 =1, 5, 25
The common factors are 1 and 5.
(c) 35 and 50
Factors of 35 = 1, 5, 7, 35
Factors of 50 = 1, 2, 5, 10, 50
The common factors are 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
The common factors are 1,2, 4, and 8.

Question 2

Find the common factors of:
(a) 4, 8 and 12 (b) 5, 15 and 25 (6) 8 9484

Answer 2

(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
The common factors are 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
The common factors are 1 and 5.

Question 3

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

Answer 3

(a) 6 and 8
multiples of 6 = 6,12,18 24,30,36,42 ,48,54,60,66,72,78,84
multiples of 8 =8, 16,24 ,32,40,48,56,64,72,80
The common multiples=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 ,126.
The common multiples=36,72,108

Question 4

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

Answer 4

Multiples 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
Multiples 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 are 12 ,24 ,36 ,48 ,60 ,72 ,84 ,96

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

Answer 5

A co-prime number have only 1 common factor

(a)18 and 35
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
The common factors= 1.
So,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 = 1.
So, they are co-prime.
(c) 30 and 415
Factors of 30 =1, 2, 3, 5, 6, 15, 30
Factors of 415 =1, 5, 83
The common factors =1 , 5
So,they are not co-prime.

(d)17 and 68
Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 68
The common factors =1,17
So,they 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
The common factor =1.
So, they are co-prime.
(f) 81 and 16
Factors of 81 =1, 3, 9, 27, 81
Factors of 16 =1, 2, 4, 8, 16
The common factor=1
So, they are co-prime.