GCF Calculator

How to use the GCF calculator

1. Enter two or more whole numbers, separated by spaces or commas.
2. Read the greatest common factor.
3. Copy the link to save or share it.

What the greatest common factor is

The greatest common factor, or GCF, is the largest whole number that divides every one of your values evenly. It is also called the greatest common divisor, so a GCD calculator does the same job, and the highest common factor. For 24 and 36, the common factors are 1, 2, 3, 4, 6, and 12, and the largest is 12, so the GCF of 24 and 36 is 12. It is the factor of two numbers that leaves no remainder in either.

How it is found

The tool uses the Euclidean algorithm, an old and efficient method. You repeatedly replace the larger number with the remainder when it is divided by the smaller, until the remainder is zero; the last non-zero value is the GCF. It is fast and exact even for very large numbers, and it extends to any number of values by taking them in pairs.

A worked example

Find the GCF of 24, 36, and 60. Start with 24 and 36: their GCF is 12. Then take 12 and 60: since 12 divides 60 exactly, the GCF is 12. So the greatest common factor of all three is 12.

FAQ

What is the greatest common factor?

It is the largest whole number that divides each of your numbers with no remainder. For 18 and 24, the GCF is 6.

Is the GCF the same as the GCD?

Yes. Greatest common factor, greatest common divisor, and highest common factor are three names for the same thing.

How do I find the GCF of two numbers?

List the factors of each and take the largest they share, or use the Euclidean algorithm as this tool does. For 20 and 30, the GCF is 10.

What is the GCF used for?

Most often for reducing fractions to lowest terms and for simplifying ratios, since dividing by the GCF gives the smallest equivalent form.

Is my information private?

Yes. Everything is calculated in your browser and nothing you enter is uploaded or saved.