Which of the following pair of …

Which of the following numbers are co-prime: (a) 18 and 35 (b) 15 and 37 (c) 30 and 415 (d) 17 and 168 (e) 216 and 215 (f) 81 and 16

Ans:

A Co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1.

(a)

Factors of 18 = 1, 2, 3, 6, 9,18

Factors of 35 = 1, 5, 7, 35

Common factor of 18 and 35 = 1

Since both have only one common factor, i.e., 1, therefore, they are co-prime numbers.

(b)

Factors of 15 = 1, 3, 5,15

Factors of 37 = 1, 37

Common factor of 15 and 37 = 1

since both have only one common factor, i.e., 1, therefore, they are co-prime numbers.

(c)

Factors of 30 = 1, 2, 3, 5, 6, 15, 30

Factors of 415 = 1, 5, 83, 415

Common factor of 30 and 415 = 1,5

Since both have more than one common factor, therefore, they are not co-prime numbers

(d)

Factors of 17 = 1, 17

Factors of 68 = 1, 2, 4, 17, 34, 86

Common factor of 17 and 68 = 1, 17

Since, both have more than one common factor, therefore, they are not co-prime numbers

(e)

Factors of 216 = 1, 2, 3, 4, 6, 8, 36, 72, 108,216

Factors of 215 = 1, 5, 43, 215

Common factor of 216 and 215 = 1

Since, both Have only one common factor, i.e , 1 , therefore they are co-prime numbers.

(f)

Factors of 81 = 1, 3, 9, 27, 81

Factors of 16 = 1, 2, 4, 8, 16

Common factor of 81 and 16  = 1

Since both have only one common factor, i.e., 1, therefore, they are co-prime numbers.