Coprime

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math

Refers to two numbers \( a \) and \( b \) if the only positive integer that is a divisor of both of them is 1. That is to say the greatest common divisor of both of them is 1, \( \gcd(a, b) \).

We describe coprimes \( a, b \) as a is coprime with b or a is prime to b.

For example 14 and 25 are coprime since \( \gcd(14, 25) = 1 \) whereas 14 and 21 are not coprime because \( \gcd (14, 21) = 7 \).

Note: If a prime number is a factor of either \( a \) or \( b \) (where \( a \) is coprime with \( b \)) then it is not a factor of the other number because the greatest common divisor of \( a, b \) is 1. They share no factors and a prime number has no factor apart from 1 and itself.