Which of the following pairs of numbers are co-prime?

(i) 25 and 105

(ii) 59 and 97

(iii) 161 and 192

(i) 25 and 105

The factors of 25 are 1, 5 and 25.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.

The common factors are 1 and 5.

Hence, 25 and 105 are not co-prime.

(ii) 59 and 97

Both 59 and 97 are prime numbers.

The only common factor is 1.

Hence, 59 and 97 are co-prime.

(iii) 161 and 192

161 = 7 × 23, so factors of 161 are 1, 7, 23 and 161.

192 = 2⁶ × 3, so factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192.

The only common factor is 1.

Hence, 161 and 192 are co-prime.