Coprime numbers, also known as relatively prime or mutually prime numbers, are two integers that have only 1 as their common factor or divisor. In other words, two numbers are coprime if the only positive integer that divides both of them is 1. For example, 4 and 9 are coprime because their greatest common divisor (GCD) is 1. The GCD of two numbers is the largest positive integer that divides both numbers without leaving a remainder.

Some properties of coprime numbers are:

• 1 is coprime with every number.
• Any two prime numbers are coprime to each other because they have only two factors, 1 and the number itself.
• The product of two coprime numbers is also coprime with each of them.
• The sum or difference of two coprime numbers is not necessarily coprime with them.

There are different ways to determine whether two numbers are coprime, such as using the Euclidean algorithm or its variants. The number of integers coprime with a positive integer n, between 1 and n, is given by Eulers totient function, also known as Eulers phi function, φ(n).