Question

Which pairs are not coprime numbers?

A)  22, 44

B)  13, 97

C)  175, 221

D)  73, 37

Answer 1

Hint: Two numbers are called co prime numbers if their common factor is 1. The two numbers need not to be prime numbers. We have to find the factors of the pair of numbers. Then we have to check the numbers that have the same factors other than 1. If they have common factors other than 1 then they are not coprime. 

Complete step-by-step answer:

We are asked if the pairs are coprime or not. Two numbers are coprime numbers if their common factor is 1. 

In option a, the numbers are 22 and 44.

22 = 1 × 2 × 11

44 = 1 × 2 × 2 × 11

As both the numbers have common factors 2 and 11. So, 22 and 44 are not co prime numbers.

In option b, the numbers are 13, 97.

13 = 1 × 13

97 = 1 × 97

As both the numbers have a common factor as 1, so 13 and 97 are coprime numbers.

In option c, the numbers are 175 and 221.

175 = 1 × 5 × 5 × 7

221 = 1 × 13 × 17 

As both the numbers have a common factor as 1, so 221 and 175 are co-prime numbers.

In option d, the numbers are 73 and 37.

73 = 1 × 73

37 = 1 × 37

As both the numbers have a common factor as 1, so they are co-prime numbers.

The answer is option a and d, as they are not coprime numbers.

Note: It is important to note the difference between prime and co-prime numbers. Two numbers are prime if they are divisible by 1 and themselves but two numbers are co-prime if they don’t have any common factors. Coprime numbers can have factors other than 1 and the number itself.