A number *n* is said to be **coprime** to *m* if the greatest common divisor of *m* and *n* is 1. Furthermore, coprime numbers have no common positive divisors other than 1.

If *m* and *n* have no common positive divisors other than 1, then *m* and *n* are coprime to each other.

For example, 5 is coprime to 8, since the divisors of 5 are 1 and 5 and the divisors of 8 are 1, 2, 4 and 8. The only common divisor that the numbers have is 1.

On the other hand, 9 is not coprime to 10, because the divisors of 9 are 1, 3 and 9 and the divisors of 10 are 1, 2, 3, 4, 6 ad 10. The common divisors of the numbers 9 and 10 are 1 and 3. Since they have a common divisor greater than 1, they are not coprime to each other.

A fraction is written in its simplest form if and only if the numerator and denominator are coprime to each other.