Greatest Common Factor Calculator

Last Updated on March 2, 2026 | 2 : 26 pm by Anas Brittany

Use this greatest common factor (GCF) calculator to find the largest number that divides two or more values evenly. Enter your numbers to instantly calculate the GCF and see how the result is determined.

What Is the Greatest Common Factor?

The greatest common factor (GCF), also called the greatest common divisor (GCD), is the largest number that divides two or more integers evenly without leaving a remainder.

For example:

Numbers: 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18

Greatest common factor = 6

How to Find the GCF

There are several methods to calculate the greatest common factor.

Method 1: Listing Factors

1. List all factors of each number
2. Identify the common factors
3. Choose the largest one

Method 2: Prime Factorization

Break each number into prime factors and multiply the common primes.

Example:

24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3

Common factors: 2 × 2 × 3 = 12

Method 3: Division Method (Euclidean Algorithm)

This method repeatedly divides numbers until the remainder is zero. It is the fastest method for large numbers and is used by most calculators.

Why the GCF Is Important

Greatest common factor is used for:

• Simplifying fractions
• Solving ratio problems
• Algebra and factoring expressions
• Measurement and grouping problems
• Number theory and mathematics

Example

Find the GCF of 24, 36, and 60:

GCF = 12

Each number can be divided by 12 evenly.

Frequently Asked Questions

What is the difference between GCF and LCM?

GCF is the largest number that divides values evenly.
LCM (least common multiple) is the smallest number that all values divide into.

Can GCF be 1?

Yes. When numbers share no common factors other than 1, they are called coprime.

Can I find the GCF of more than two numbers?

Yes. The greatest common factor can be calculated for any number of integers.