Class 6 Maths NCERT Solutions for Chapter 3 Playing with Numbers Ex 3.4

Playing with Numbers

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) We have, 20 = 1 x 20
= 2 x 10
= 4 x 5
∴ All the factors of 20 are 1, 2, 4, 5, 10 and 20
Again, 28 = 1 x 28
28 = 2 x 14
28 = 4 x 7
∴ All the factors of 28 are 1, 2, 4, 7, 14 and 28.
Out of these 1, 2 and 4 occur in both the lists.
∴ 1, 2 and 4 are common factors of 20 and 28.

(b) We have, 15 = 1 x 15
15 = 3 x 5
∴ All the factors of 15 are 1, 3, 5 and 15.
Again, 25 = 1 x 25
25 = 5 x 5
∴ All the factors of 25 are 1, 5 and 25.
Out of these 1 and 5 occur in both the lists.
∴1 and 5 are common factors of 15 and 25.

(c) We have, 35 = 1 x 35
35 = 5 x 7
∴ All the factors of 35 are 1, 5, 7 and 35.
Again, 50 = 1 x 50
50 = 2 x 25
50 = 5 x 10
∴ All the factors of 50 are 1, 2, 5, 10, 25 and 50. ,
Out of these 1 and 5 occur in both the lists.
∴ 1 and 5 are common factors of 35 and 50.

(d) We have, 56 = 1 x 56
56 = 2 x 28
56 = 4 x 14
56 = 7 x 8
∴ All the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
Again, 120 = 1 x 120
120 = 2 x 60
120 = 3 x 40
120 = 4 x 30
120 = 5 x 24
120 = 6 x 20
120 = 8 x 15
120 = 10 x 12
∴ All the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Out of these 1, 2, 4 and 8 occur in both the lists.
∴ 1, 2, 4 and 8 are common factors of 56 and 120.

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

Solution:
(a) We have, 4=1 x 4
4 = 2 x 2
∴ All the factors of 4 are 1, 2 and 4.
Again, 8 = 1 x 8
8 = 2 x 4
∴All the factors of 8 are 1, 2, 4 and 8.
Again, 12 = 1 x 12
12 = 2 x 6
12 = 3 x 4
∴ All the factors of 12 are 1, 2, 3, 4, 6 and 12.
Out of these 1, 2 and 4 occur in all the three lists.
∴ 1, 2 and 4 are common factors of 4, 8 and 12.

(b) We have, 5 = 1 x 5
∴All the factors of 5 are 1 and 5.
15 = 1 x 15
15 = 3 x 5
∴ All the factors of 15 are 1, 3, 5 and 15.
25 = 1 x 25
25 = 5 x 5
∴ All the factors of 25 are 1, 5 and 25.
Out of these 1 and 5 occur in all the three lists.
∴ 1 and 5 are common factors of 5, 15 and 25.

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

Solution:
(a) Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72,…
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72,…
Out of these 24, 48, 72, … occur in both thfe lists.
∴ The first three common multiples of 6 and’8 are 24, 48 and 72.
(b) Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, …
Multiples of 18 are 18, 36, 54, 72, 90, 108, …
Out of these 36, 72, 108, … occur in both the lists.
∴ The first three common multiples of 12 and 18 are 36, 72 and 108.

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

Solution:
Common multiples of 3 and 4 are multiples of 3 x 4 i. e., 12.
∴ Common multiples of 3 and 4 less than 100 are 12, 24, 36,48, 60, 72, 84 and 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

Solution:
(a) Factors of 18 are 1, 2, 3, 6, 9 and 18 and, that of 35 are 1, 5, 7 and 35.
∴ Common factor of 18 and 35 is 1.
Thus, 18 and 35 are co-prime.

(b) Factors of 15 are 1, 3, 5 and 15 and, that of 37 are 1 and 37.
∴ Common factor of 15 and 37 is 1.
Thus, 15 and 37 are co-prime.

(c) Since 5 is a common factor of 30 and 415.
∴ 30 and 415 are not co-prime.

(d) ∴ 68 + 17 = 4 i.e., 17 is a common factor of 17 and 68.
∴ 17 and 68 are not co-prime.

(e) Since 1 is the only common factor of 216 and 215.
∴ 216 and 215 are co-prime.

(f) Since 1 is the only common factor of 81 and 16.
∴ 81 and 16 are co-prime.

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

Solution:
Since a number is divisible by both 5 and 12.
So, it is also divisible by 5 x 12 i. e., 60.

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

Solution:
Factors of 12 are 1, 2, 3, 4 and 12.
Since a number is divisible by 12. So, it is also divisible by the factors of 12.
Thus, the number is also divisible by 2, 3 and 4.

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