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.

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