Greatest Common Factor Calculator

What Is the Greatest Common Factor?

The greatest common factor (GCF), also called the greatest common divisor (GCD), is the largest positive number that divides evenly into every number in a set. It's used to simplify fractions to their lowest terms and to break a group of numbers down into their shared building blocks.

How It's Calculated

This calculator uses the Euclidean algorithm, which repeatedly replaces the larger of two numbers with the remainder of dividing it by the smaller one until the remainder is zero - at that point the other number is the GCF. For more than two numbers, it finds the GCF pairwise and combines the results.