Haryana State Board HBSE 6th Class Maths Solutions Chapter 3 Playing With Numbers Ex 3.4 Textbook Exercise Questions and Answers.
Haryana Board 6th Class Maths Solutions Chapter 3 Playing With Numbers Exercise 3.4
Question 1.
Find the common factor of:
(a) 20 and 28
(b) 15 and 25
(c) 35 and 50
(d) 56 and 120.
Solution:
(a) 20 = 1 × 20
=2 × 10
=4 × 5
28 = 1 × 28
= 2 × 14
= 4 × 7
∴ Factors of 20 are : 1, 2, 4, 5, 10, 20.
∴ Factors of 28 are : 1, 2, 4, 7, 14, 28.
Hence, common factors of 20 and 28 are: 1, 2, 4.
(b) 15 = 1 × 15
= 3 × 5
25 = 1 × 25
= 5 × 5
∴ Factors of 15 are: 1, 3, 5, 15.
Factors of 25 are: 1, 5, 25.
Hence, common factors of 15 and 25 are: 1, 5 .
(c) 35 = 1 × 35
= 5 × 7
50 = 1 × 50
= 2 × 25
= 5 × 10
∴ Factors of 35 are: 1, 5, 7, 35.
Factors 50 are : 1, 2, 5, 10, 25, 50.
Hence, common factors of 35 and 50 are: 1, 5.
(d)
56 = 1 × 56
= 2 × 28
= 4 × 14
= 7 × 8
120 = 1 × 120
= 2 × 60
= 3 × 40
= 4 × 30
= 5 × 24
= 6 × 20
= 8 × 15
= 10 × 12
∴ Factors of 56 are : 1, 2, 4, 7, 8, 14, 28, 56.
Factors of 120 are : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Hence, common factors of 56 and 120 are : 1, 2, 4, 8.
Question 2.
Find the common factors of:
(a) 4, 8 and 12 (b) 5, 15 and 25.
Solution:
4 = 1 × 4
= 2 × 2
8 = 1 × 8
= 2 × 4
12,= 1 × 12
= 2 × 6
= 3 × 4
∴ Factors of 4 are : 1, 2, 4.
Factors of 8 are : 1, 2, 4, 8.
Factors of 12 are : 1, 2, 3, 4, 6, 12.
Hence, common factors of 4, 8 and 12 are : 1, 2, 4.
(b)
5 = 1 × 5
15 = 1 × 15
= 3 × 5
25 = 1 × 25
= 5 × 5
∴ Factors of 5 are : 1, 5.
Factors of 15 are : 1, 3, 5, 15.
Factors of 25 are : 1, 5, 25.
Hence, common factors of 5, 15 and 25 are : 1, 5.
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, 80,
Hence, first three common multiples of 6 and 8 are : 24, 48, 72,………
(b) Multiples of 12 are : 12, 24, 36, 48, 60,
72, 84, 96, 108, 120,
Multiples of 18 are : 18, 36, 54, 72, 90, 108, 126, 144, 162,180, ……….
Hence, first three multiples of 12 and 18 are : 36, 72, 108…….
Question 4.
Write all the numbers less than 100 which are common multiples of 3 and 4.
Solution:
Multiples of 3 less than 100 are : 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 less than 100 dre : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96.
Henee, common multiples of 3 and 4 less than 100 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.
Solution:
(a) 18 = 1 × 18
=2 × 9
= 3 × 6
35 = 1 × 35
=5 × 7
∴ Factors of 18 are : 1, 2, 3, 6, 9, 18.
Factors of 35 are : 1, 5, 7, 35.
∵ Common factor of 18 and 35 is 1 only. Hence, 18 and 35 are co-primes.
(b) 15 = 1 × 15 37 = 1 × 37
= 3 x 5
∴ Factors of 15 are : 1, 3, 5, 15.
Factors of 37 are : 1, 37.
∵ Common factor of 15 and 37 is 1 only.
Hence, 15 and 37 are co-prime.
(c) 30 = 1 × 30
= 2 × 15
= 3 × 10
= 5 × 6
415 = 1 × 415
= 5 × 83
∴ Factors of 30 are : 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 415 are : 1, 5, 83, 415.
∵ Common factor of 30 and 415 are 1, 5.
Hence, 30 and 415 are not co-prime.
(d) 17 = 1 × 17
68 = 1 × 68
= 2 × 34
= 4 × 17
∴ Factors of 17 are : 1, 17.
Factors of 68 are : 1, 2, 4, 17, 34, 68.
∵ Common factor of 17 and 68 are : 1, 17.
Hence, 17 and 68 are not co-prime.
(e) 216 = 1 × 216
= 3 × 72
= 4 × 54
= 6 × 36
= 8 × 27
= 9 × 24
= 12 × 18
215 = 1 × 215
= 5 × 43
∴ Factors of 216 are : 1, 3, 4, 6, 8, 9, 12,
18, 24, 27, 36, 54, 72, 216.
Factors of 215 are : 1, 5, 43, 215.
∵ Common factor of 216 and 215 is 1 only. Henoa 216 and 215 are co-prime.
(f) 81 = 1 × 81
= 3 × 27
=9 × 9
16 = 1 × 16
=2 × 8
=4 × 4
∴ Factors of 81 are : 1, 3, 9, 27, 81.
Factors of 16 are : 1, 2, 4, 8, 16.
∵ Common factor of 81 and 16 is 1 only.
Hence, 81 and 16 are co-prime.
Question 6.
A number is divisible by both 5 and 12. By which other number will that number always be divisible ?
Solution:
∵ 5 and 12 are co-prime.
∴ A number divisible by bpth 5 and 12 will always be divisible by their product i.e. 5 × 12 = 60.
Question 7.
A number is divisible by 12. By what other numbers will that number be divisible ?
Solution:
12 = 1 × 12
= 2 × 6
= 3 × 4
Factors of 12 other than 12 are : 1, 2, 3, 4, 6.
Hence, if a number is divisible by 12, it will also be divisible by 1, 2, 3, 4 and 6.