Question

# 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

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Solution

## (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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