Which of the following is coprime?
a)13 and 14    b) 8 and 20     c) 31 and 59     d) 34 and 85

Solution:

Two numbers or integers are co-prime if their common factor is only 1 or co-prime numbers are the set of numbers whose highest common factor is 1

a) 13 and 14

They have only 1 as their common factor

So, their HCF is 1

Hence, they are co-prime numbers

b) 8 and 20

We have common factors of 8 and 20 i.e.,2,4

So, their HCF is 4

Hence, they are not co-prime numbers

c) 31 and 59

They have only 1 as their common factor

So, their HCF is 1

Hence, they are co-prime numbers

d) 34 and 85

We have a common factor of 34 and 85 i.e.,17

So, their HCF is 17 

Hence, they are not co-prime numbers

Therefore, the pair of co-prime numbers are: a) 13 and 14 and c) 31 and 59

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Which of the following is coprime? a)13 and 14 b) 8 and 20 c) 31 and 59 d) 34 and 85

Summary:

The co-prime numbers are a) 13 and 14 and c) 31 and 59.