EXERCISE 3.4
1). Find the common factors of:
a) 20 and 28
Ans.
Factors of
20 = 1, 2, 4, 5, 10 and 20
28 = 1, 2, 4, 7, 14 and 28 ∴ the common factors are 1, 2, 4
b) 15 and 25
Ans.
Factors of
15 = 1, 3, 5 and 15
25 = 1, 5 and 25
∴ common factors are 1, 5.
c) 35 and 50
Ans.
Factors of
35 = 1, 5, 7 and 35
50 = 1, 2, 5, 10, 25 and 30
∴ e the common factors are 1, 5
d) 56 and 120
Ans.
Factors of
56 = 1, 2, 4, 7, 8, 14, 28 and 56
120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
∴ the common factors are 1, 2, 4, 8
2). Find the common factors of :
a) 4, 8 and 12
Ans.
Factors of
4 = 1, 2, 4
8 = 1, 2, 4, 8
12 = 1, 2, 3, 4, 6, 12
therefore, common factors are 1, 2, 4.
b) 5, 15 and 25
Ans.
Factors of
5 = 1, 5
15 = 1, 3, 5 and 15
25 = 1, 5, 25
therefore, common factors are 1, 5.
3) Find the first three common multiples of:
a) 6 and 8
Ans.
Multiples of
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
8 = 8, 16, 24, 32, 40, 48, 56, 64, 72
∴ the first three common multiples are 24, 48, 72.
b) 12 and 18
Ans.
Multiple of
12 = 12, 24, 36, 48, 60, 72, 84, 96, 108
18 = 18, 36, 54, 72, 90, 108
∴ the first three common multiples are 36, 72, 108.
4). Write all the numbers less than 100 which are common multiples of 3 and 4
Ans.
Multiples of 3 less than 100 are
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 less than 100 are
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
the common multiples are = 12, 24, 36, 48, 60, 72, 84, 96
5). Which of the following numbers are co-prime :
a) 18 and 25
Ans.
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factor = 1
∴ 18 and 35 are co-prime.
b) 15 and 37
Ans.
Factors of 15 = 1, 3, 5, 15
Factors of 37 = 1, 3, 7
Common factor = 1
∴ 15 and 37 are co-prime.
c) 30 and 415
Ans.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 415 = 1, 5, 53, 415
Common factors = 1, 5 ∴ 30 and 415 are not co-prime.
d) 17 and 68
Ans.
Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 68
common factors = 1, 17
∴ 17 and 68 are not co-prime.
e)216 and 215
Ans.
Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54
Factors of 215 = 1, 5, 43, 215
Common factors = 1
∴ 216 and 215 are co-prime
d) 81 and 16
Ans.
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common factor = 1
∴ 81 and 16 are co-prime.
6). A number is divisible by both 5 and 12. By which other number will that number always be divisible?
Ans.
Factors of 5 are = 1, 5
Factors of 12 are = 1, 2, 3, 4, 6, 12
Common factor = 1
∴ both numbers are co-prime and is also divisible by the product 60
because 5 x 12 = 60
7). A number is divisible by 12. By what other numbers will that number be divisible?
Ans.
Since the number is divisible by 12, it is also divisible by its factors of 12.The factors of 12 are 1, 2, 3, 4, 6, 12. So the numbers are 1, 2, 3, 4, 6 other than 12.