On this page is a *greatest common factor calculator*, often abbreviated as GCF. This term goes by many names – it is also known as the greatest common divisor (GCD) and highest common factor (HCF).

Enter a set of numbers and the GCF tool will return the greatest common factor. While the tool will accept negatives and decimals, you should use positive integers.

*Looking for a similar tool? Try one of these instead:*

## Greatest Common Factor (GCF) Calculator

**Table of Contents**show ▼

## What is the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD)?

The *Greatest Common Factor* (GCF) or Greatest Common Divisor (GCD) of a set of positive integers is the biggest positive integer which can evenly divide each number. That is: it is a positive number which can divide each number in the set and leave an integer.

## Finding the Greatest Common Factor

By hand, you can find the greatest common denominator by finding each number's prime factorization – that is, the prime numbers which when multiplied together make up the number.

For example, let's use the numbers in the calculator: 14, 21, 49, and 70:

And as you can see above, the largest factor that appears for all four is **7**.

## Using the Greatest Common Factor Calculator

In the text box at the top, enter a list of numbers where you'd like us to find the greatest common factor. You can enter whole numbers, fractions, negatives, and decimals – but it makes the most sense to enter positive integers.

When done, hit the **Compute GCF** button. We'll return both the Greatest Common Factor we calculate, plus the number of input numbers we understood for you to check the work.

*Like this? Visit our other calculators and tools.* See also our factor calculator and prime factorization calculator.