What Are Relatively Prime Numbers?

Two numbers are relatively prime if they have no common divisors other than 1 or -1. It is not possible to divide both numbers by a common value to produce a whole number.

For example, 20 and 9 are relatively prime because the only number they can both be evenly divided by is 1 (in other words, 1 is their greatest common factor). On the other hand, 21 and 9 are not relatively prime because you can divide both numbers by 3.

As another example, -12 and -13 are relatively prime as the only numbers they can both be evenly divided by are 1 and -1 (having two divisors still makes the two numbers relatively prime). But -15 and -5 can be divided by 5, 3, -5 and -3, and so are not relatively prime.

The concept of relatively prime numbers turns up in other number theory formulas. For example, consecutive positive integers are consistently relatively prime. This pattern can be demonstrated using any two consecutive positive numbers. As seen before, 12 and 13 are relatively prime. Similarly, 34 and 35 are relatively prime. Even 100,000 and 100,001 are relatively prime. The number of pairs that are relatively prime is infinite.