# What Are Relatively Prime Numbers? - Examples & Calculations

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Lesson Transcript
Instructor: Joshua White

Josh has worked as a high school math teacher for seven years and has undergraduate degrees in Applied Mathematics (BS) & Economics/Physics (BA).

This lesson will examine relatively prime numbers, including the definition of them and how to determine if two numbers are relatively prime. It will also cover the greatest common factor and least common multiple of relatively prime numbers.

## What Are Relatively Prime Numbers?

Perhaps you have met someone who you thought shared the same interests as you, but upon further discovery you found out you didn't really have anything in common with this person. For example, maybe you met someone at the gym and this person said that he/she loves to go traveling, watch sports, and exercise. That sounds great, since you like doing those same things as well.

However, when you started talking to the person, you found out that his/her idea of traveling is camping and hiking out in the wilderness and he/she enjoys playing and watching golf and tennis. You, on the other hand, prefer traveling overseas to large metropolitan cities and love playing and watching team sports like softball and soccer. Thus, it turns out that you actually have nothing in common with this person after all. A similar scenario happens in math with relatively prime numbers.

Two numbers are relatively prime, or co-prime, if they have no factors in common other than 1. An alternate way to state this is that two relatively prime numbers have a greatest common factor, or GCF, of 1. Additionally, the least common multiple, or LCM, of two relatively prime numbers can be found by multiplying the numbers together, because, by definition, the numbers have no factors in common. Please note the numbers themselves do not need to be prime in order for the pair to be relatively prime; all that matters is how the factors of the numbers are related to each other.

But how do you tell if two numbers are relatively prime?

## How to Check if Numbers Are Relatively Prime

To determine if two numbers are relatively prime, you need to first factor each number into its prime factors; hopefully you remember that this is also called prime factorization. Then you will compare these factors to see if any of them are found in both numbers. If none of the factors are in common, other than 1, then the numbers are relatively prime and their GCF is 1. However, if there is at least one common factor, then the numbers are not relatively prime.

Let's take the numbers 28 and 45. Are they relatively prime?

Prime factorization of 28 equals: 1 * 2 * 2 * 7

Prime factorization of 45 equals: 1 * 3 * 3 * 5

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