Greatest Common Factor

First Number: Second Number: Third Number:
If you only want to do two numbers, leave the Third Box empty.

is the Greatest Common Factor (GCF)

Find the Greatest Common Factor (GCF) of a group of two or three numbers.

Table of contents:

What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF) between two or more numbers is the largest natural number that divides all of those numbers simultaneously.

When two or more numbers have a GCF equal to 1, these numbers will be said to be prime to each other or co-prime.

How to find the Greatest Common Factor (GCF)?

Method 1: the dividers

As we are looking for the greatest common divisor, we can simply list the divisors of the numbers studied and locate the greatest of the divisors common to these numbers. This simple method is especially suitable when you have small numbers.

Method 2: the table of prime divisors

This method consists of simultaneously dividing the studied numbers by prime divisors. The GCF will then be the product of these prime dividers. This method is faster and more efficient when looking for the GCF between two large numbers.

Method 3: prime factors

This method consists of doing the first factorization of all the numbers and writing the GCF as a common product of the factors.