Definition of Coprime

We say that two positive integers are coprime if they have no common positive factors other than \(1\).

A pair of different prime numbers is always coprime.

For example, the integers \(22\) and \(25\) are coprime:

• The factors of \(22\) are \(1,2,11\) and \(22\).
• The factors of \(25\) are \(1,5\) and \(25\).
• The only factor in both of these lists is \(1\).

The integers \(12\) and \(24\) are not coprime:

• The factors of \(12\) are \(1,2,3,4,6\) and \(12\)
• The factors of \(24\) are \(1,2,3,4,6,8,12\) and \(24\)
• The common factors of \(12\) and \(24\) are \(1,2,3,4,6\) and \(12\).

Some other terms for "coprime" are "relatively prime" and "mutually prime".