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Greatest Common Factor Calculator

Find the greatest common factor, also called the GCD or HCF, of two or more numbers. See Euclid's algorithm step by step and the list of common factors.

Formulas last reviewed: September 2026

Disclaimer: Results are calculated with standard formulas and are meant for learning and quick checks. Please double-check important work, especially anything used for exams, engineering, finance or safety.

The largest number that divides them all

The greatest common factor (GCF), also called the greatest common divisor (GCD) or highest common factor (HCF), is the largest whole number that divides all the numbers in a list without a remainder. It is the key to simplifying fractions and ratios.

This calculator finds the GCF of up to ten numbers, shows Euclid's algorithm step by step and lists the common factors.

How it is calculated

Euclid: GCF(a, b) = GCF(b, a mod b)
Repeat until the remainder is 0

Worked example

GCF of 48 and 180

Step 1
180 = 3 × 48 + 36
Step 2
48 = 1 × 36 + 12
Step 3
36 = 3 × 12 + 0
Step 4
GCF = 12
GCF
12

Uses of the GCF

  • Simplify 48/180 by dividing both by 12 to get 4/15.
  • Split items into the largest equal groups with nothing left over.
  • Reduce a ratio such as 48 : 180 to 4 : 15.

A practical use

If you have 48 red and 180 blue tiles and want to split them into identical groups with none left over, the largest number of groups you can make is the GCF of 48 and 180 — 12 groups, each with 4 red and 15 blue tiles.

Frequently asked questions

Are GCF, GCD and HCF the same thing?

Yes. Different countries and textbooks use different names for the same number.

What is the GCF of two coprime numbers?

Numbers that share no factor other than 1 are called coprime, and their GCF is 1, for example 8 and 15.

What is the GCF if one number is zero?

The GCF of a number and zero is that number itself. This calculator asks for positive whole numbers.

Why does Euclid's algorithm work?

Any number that divides both a and b also divides the remainder of a divided by b, so the pair can be reduced without changing the GCF.