# 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

(a) 18 and 35

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)15 and 37

Factors of 15=1,3,5,15

Factors of 37=1,37

Common factors =1

Therefore, the given two numbers are co-prime.

(c) 30 and 415

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 non co-prime.

(d) 17 and 68

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 non 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

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