Common Factor Calculator

Find all common factors shared by two numbers and the greatest common factor

About the Common Factor Calculator

This common factor calculator finds all positive integers that divide evenly into both of two given numbers. It lists each number's factors, highlights the shared (common) ones in green, and identifies the greatest common factor (GCF). Understanding common factors is essential for simplifying fractions and solving ratio problems.

How It Works

Common factors of a and b = Factors(a) \u2229 Factors(b)

The calculator first finds all factors of each number individually, then identifies the intersection of the two sets. The largest number in this intersection is the GCF. For example, common factors of 36 and 48 are 1, 2, 3, 4, 6, 12 and the GCF is 12.

Frequently Asked Questions

What is the difference between a common factor and the GCF?

A common factor is any factor that divides both numbers evenly. The GCF (Greatest Common Factor) is the largest of these common factors. For example, 1, 2, 3, and 6 are all common factors of 12 and 18, but the GCF is 6.

Can two numbers have no common factors?

Every pair of positive integers has at least one common factor: 1. Numbers whose only common factor is 1 are called coprime (or relatively prime). For example, 8 and 15 are coprime because their only common factor is 1.