Question

Which of the following is a pair of co-primes?
(a) (14, 35)
(b) (18, 25)
(c) (31, 93)
(d) (32, 62)

Answer 1

Hint: Co-prime number is a set of numbers or integers which have only 1 as their common factor that means their highest common factor (HCF) will be 1.

Complete step-by-step answer:
Consider a set of two numbers, if they have no positive integer that can divide both, other than 1, the pair of numbers is co-prime.
For option (a), 14 and 35:
The factors of 14 are 1, 2 and 7 and the factors of 35 are 1, 5 and 7.
Here 14 and 35 have two common factors: they are 1 and 7. Hence, their HCF is 7 and they are not co-prime.
For option (b), 18 and 25:
The factors of 18 are 1, 2, 3, 6 and 9 and the factors of 25 are 1 and 5.
Here 18 and 25 have only one common factor that is 1. Hence, their HCF is 1 and they are co-prime.
For option (c), 31 and 93:
The factors of 31 are 1 and 31 and the factors of 93 are 1, 3 and 31.
Here 31 and 93 have two common factors: they are 1 and 31. Hence, their HCF is 31 and they are not co-prime.
For option (d), 32 and 62:
The factors of 32 are 1, 2, 4, 8 and 16 and the factors of 62 are 1, 2 and 31.
Here 14 and 35 have two common factors: they are 1 and 2. Hence, their HCF is 2 and they are not co-prime.
Hence, the correct option is (b)

Note:The possibility for the mistake is that you might get confused with the difference between prime and co-prime numbers. A prime number is defined as a number which has no factor other than 1 and itself. On the contrary, co-primes are considered in pairs and two numbers are co-prime if they have no common factors other than 1.