Chapter 3 Playing With Numbers 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) Given numbers are : 20 and 28
Factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 28 are 1, 2, 4, 7, 28
Hence, the common factors are 1, 2 and 4.
(b) Given numbers are: 15 and 25
Factors of 15 are 1, 3, 5, 15
Factors of 25 are 1, 5, 25
Hence, the common factors are 1 and 5.
(c) Given numbers are: 35 and 50
Factors of 35 are: 1, 5, 7, 35
Factors of 50 are: 1, 2, 5, 10, 50
Hence, the common factors are 1 and 5.
(d) Given numbers are: 56 and 120
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, 30, 40, 60, 120
Hence, 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
Solution:
(a) Given numbers are: 4, 8 and 12
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, the common factors are 1, 2 and 4.
(b) Given numbers are: 5, 15 and 25
Factors of 5 are 1, 5
Factors of 15 are 1, 3, 5, 15
Factors of 25 are 1, 5, 25
Hence, the common factors are 1 and 5.
Question 3.
Find first three multiples of:
(a) 6 and 8
(b) 12 and 18
Solution:
(a) Given numbers are 6 and 8
First three multiples of 6 are
6 x 1= 6; 6 x 2 = 12; 6 x 3 = 18.
First three multiples of 8 are
8 x 1 = 8; 8 x 2 = 16; 8 x 3 = 24.
(b) Given numbers are 12 and 18.
First three multiples of 12 are
12 x 1 = 12;
12 x 2 = 24;
12 x 1 = 36;
First three multiples of 18 are
18 x 1 = 18;
18 x 2 = 36;
18 x 3 = 54.
Question 4.
Write all the numbers less than 100 which are common multiples of 3 and 4.
Solution:
Given numbers are 3 and 4.
Multiples of 3 less than 100 are:
Hence, the 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) Given number are 18 and 35
Factors of 18 are 1, 2, 3, 6, 9, 18
Factors of 35 are 1, 5, 7, 35
Since, the common factors of 18 and 35 is only 1.
Hence, 18 and 35 are co-prime.
(b) Given numbers are 15 and 37
Factors of 15 are 1, 3, 5, 15
Factors of 37 are 1,37
Since, the common factor of 15 and 37 is only 1.
Hence, they are co-prime.
(c) Given numbers are 30 and 415
Factors of 30 are 1, 2, 3, 5, 6, 15, 30
Factors of 415 are 1, 5, 83
Since, the numbers have common factors 1 and 5
Hence, they are not co-prime.
(d) Given numbers are 17 and 68
Factors of 17 are 1, 17
Factors of 68 are 1, 2, 4, 17, 34, 68
Since, the numbers have common factors 1 and 17
Hence, they are not co-prime.
(e) Given numbers are 216 and 215
Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 54, 72, 108, 216
Factors of 215 are 1, 5, 43
Since only 1 is the common factor of 216 and 215.
Hence, they are co-prime.
(f) Given numbers are 81 and 16
Factors of 81 are 1, 3, 9, 27, 81
Factors of 16 are 1, 2, 4, 8, 16
Since only 1 is common to 81 and 16
Hence, they are co-prime.
Question 6.
A number is divisible by both 5 and 12. By which other will that number be always divisible?
Solution:
If the number is divisible by both 5 and 12 this the number will also be divisible by 5 x 12 i.e., 60.
Question 7.
A number is divisible by 12. By what other will that number be divisible?
Solution:
Factors of 12 are 1, 2, 3, 4, 6, 12
Hence the number which is divisible by 12, will also be divisible by its factors i.e., 1, 2, 3, 4, 6 and 12.