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
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) 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.
