Greatest Common Factor (GCF) Calculator

Discover the GCF of multiple numbers quickly and easily. Enter numbers to get started!

Enter Numbers

Input a list of positive integers separated by commas (e.g., 12, 18, 24).

Result:

GCF Visualization

Understanding the Greatest Common Factor. Below are the factors of each number you entered.

The Greatest Common Factor (GCF) of the numbers is:

Understanding Greatest Common Factor (GCF)

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the integers. For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

How to find GCF: One common method to find the GCF of two or more numbers is by listing the factors of each number and identifying the largest factor they have in common. For instance, factors of 12 are 1, 2, 3, 4, 6, 12, and factors of 18 are 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3, 6, and the greatest among them is 6.

Mathematically, for two numbers a and b, GCF can be represented using various notations. One common formula relating GCF and Least Common Multiple (LCM) is:

$$ GCF(a, b) imes LCM(a, b) = |a imes b| $$
$$ GCF(a, b) = rac{|a imes b|}{LCM(a, b)} $$

This calculator simplifies the process of finding the GCF for you, making it easier to understand and verify your calculations.

Learn more about GCF on Wikipedia.