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Find the common factors of:
(a) 20 and 28 (b) 15 and 25
(c) 35 and 50 (d) 56 and 120
a) factors of 20= 1,2,4,5,10,20
Factors of 28= 1,2,4,7,14,28
Common factors = 1,2,4
b) factors of 15= 1,3,5,15
Factors of 25 = 1,5,25
Common factors= 1,5
c) factors of 35 = 1,5,7,35
Factors of 50= 1,2,5,10,25,50
Common factors = 1,5
d) factors of 56= 1,2,4,7,8,14,28,56
Factors of 120= 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Common factors=1,2,4,8
Find the common factors of:
(a) 4, 8 and 12 (b) 5, 15 and 25
(a) 4, 8, 12
Factors of 4 = 1, 2, 4
Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Common factors = 1, 2, 4
(b) 5, 15, and 25
Factors of 5 = 1, 5
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors = 1, 5
Find first three common multiples of:
(a) 6 and 8 (b) 12 and 18
(a) 6 and 8
Multiple of 6 = 6, 12, 18, 24, 30…..
Multiple of 8 = 8, 16, 24, 32……
3 common multiples = 24, 48, 72
(b) 12 and 18
Multiples of 12 = 12, 24, 36, 48
Multiples of 18 = 18, 36, 54, 72
3 common multiples = 36, 72, 108
Write all the numbers less than 100 which are common multiples of 3 and 4.
Multiples of 3 = 3, 6, 9, 12, 15…
Multiples of 4 = 4, 8, 12, 16, 20…
Common multiples = 12, 24, 36, 48, 60, 72, 84, 96
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
(a) Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factor = 1
Therefore, the given two numbers are co-prime.
(b) Factors of 15 = 1, 3, 5, 15
Factors of 37 = 1, 37
Common factors = 1
Therefore, the given two numbers are co-prime.
(c) Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 415 = 1, 5, 83, 415
Common factors = 1, 5
As these numbers have a common factor other than 1, the given two numbers are not co-prime.
(d) Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 68
Common factors = 1, 17
As these numbers have a common factor other than 1, the given two numbers are not co-prime.
(e) 216 and 215
Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Factors of 215 = 1, 5, 43, 215
Common factors = 1
Therefore, the given two numbers are co-prime.
(f) 81 and 16
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common factors = 1
Therefore, the given two numbers are co- prime.
A number is divisible by both 5 and 12. By which other number will that number be always divisible?
Factors of 5 = 1, 5
Factors of 12 = 1, 2, 3, 4, 6, 12
As the common factor of these numbers is 1, the given two numbers are co- prime and the number will also be divisible by their product, i.e. 60, and the factors of 60, i.e., 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
A number is divisible by 12. By what other number will that number be divisible?
Since the number is divisible by 12, it will also be divisible by its factors i.e., 1, 2, 3, 4, 6, 12. Clearly, 1, 2, 3, 4, and 6 are numbers other than 12 by which this number is also divisible.
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