## What Is A Relative Prime Also Known As A Co-Prime?

If two numbers have no common factors i.e. there Greatest Common
Factor is one, they are called **Relative Primes**; In
other words, both numbers cannot evenly divide both by the same common value. For example
the numbers 40 and 21 are called Relative Prime even those they
are Composite Numbers. Below is an
example:

As you can see the prime factors of 40 and 21 follow:

- 40 = 1 x 2 x 2 x 2 x 5 = 4 x 10 = 8 x 5 -> factors are 1, 2, 4, 5, 8, 40
- 21 = 1 x 3 x 7 -> factors are 1, 3, 7, and 21

There is no common divisor other than one or the number itself. That means 21 and 40 Relative-Prime also known as **Co-Primes**.

As you can see the prime factors of 21 and 24 follow:

- 21 = 1 x 3 x 7 -> factors are 1, 3, 7, and 21
- 24 = 1 x 2 x 3 x 4 = 3 x 8 = 4 x 6 -> factors are 1, 2, 3, 4, 6, 8, and 24

The numbers 1 and 3 are common factors. That means 21 and 40 are NOT relative-primes and NOT co-primes.