Co-prime numbers, also known as relatively prime or mutually prime numbers, are pairs of numbers that do not have any common factor other than 1. In other words, two integers a and b are coprime if the only positive integer that is a divisor of both of them is 1. When two numbers are coprime, their greatest common divisor is 1, which can be expressed mathematically as gcd(a, b) = 1 or (a, b) = 1.
Some properties of co-prime numbers include:
- 1 is co-prime with every number.
- Any two prime numbers are co-prime to each other, as every prime number has only two factors, 1 and the number itself, and the only common factor of two prime numbers is 1.
- A set of integers can also be called coprime if its elements share no common positive factor except 1.
- Co-prime numbers can also be composite numbers (a number with more than two factors) if their common factor is 1.
It is important to note that two numbers do not have to be prime numbers to be coprime numbers.
