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Greatest Common Factor Calculator

GCF by prime factorisation and the Euclidean algorithm.

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Separate with commas or spaces. GCF, GCD and HCF all mean the same thing.

Method 1 — prime factorisation

Multiply every shared prime, raised to the lowest power it appears at.

NumberPrime factorisation

Method 2 — the Euclidean algorithm

Divide, keep the remainder, repeat. When the remainder hits zero, the last non-zero value is the answer.

StepDivisionRemainder

Greatest common factor

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Related values

Least common multiple—
Product of the numbers—
Euclidean steps—
Coprime?—

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Your numbers reduced to lowest terms

For two numbers, GCF × LCM equals their product — which is why the LCM can be found by dividing the product by the GCF. The Euclidean algorithm is what you would use on large numbers: it needs only repeated division and finishes in a handful of steps even for values with hundreds of digits.

Quick Tool Overview

The Greatest Common Factor Calculator finds the largest number dividing all of your numbers exactly, worked out both by prime factorisation and by the Euclidean algorithm, with every step of each method shown.

What it does
Finds the GCF of two or more numbers, two ways
You give it
Two or more whole numbers
You get back
The GCF plus both methods worked through
Best for
Simplifying fractions and coursework that wants the method
Calculators Free, unlimited use No sign-up Runs in your browser

About the Greatest Common Factor Calculator

Find the largest number that divides evenly into all of your numbers, worked out two different ways. Prime factorisation shows which shared primes contribute and at what power; the Euclidean algorithm shows the sequence of remainders that converges on the answer.

Both methods are included because they teach different things. Factorisation makes the structure visible — the GCF is the product of every shared prime raised to the lowest power it appears at — while the Euclidean algorithm is what you would actually use on large numbers, since it needs only repeated division and finishes in a handful of steps even for values with hundreds of digits. Greatest common factor, greatest common divisor and highest common factor are three names for the same thing.

Key features of the Greatest Common Factor Calculator

Two methods, both shown

Prime factorisation makes the structure visible; the Euclidean algorithm is what you would use on large numbers.

Euclidean steps listed

Each division and remainder is printed, so the sequence converging on the answer is legible.

Shared primes marked

The factorisation view highlights which primes are common and at what lowest power.

Handles many numbers

The GCF is taken pairwise across the whole set, not just two values.

Names reconciled

GCF, GCD and HCF are three names for the same thing, and the page says so up front.

How to use the Greatest Common Factor Calculator

  1. 1

    Enter your numbers

    Two or more whole numbers, separated by commas or spaces.

  2. 2

    Read the GCF

    The largest number dividing all of them exactly.

  3. 3

    Follow the factorisation

    Each number's prime factorisation, with the shared primes and lowest powers marked.

  4. 4

    Follow the Euclidean steps

    The division sequence that reaches the same answer without factorising anything.

Frequently asked questions

The largest whole number that divides evenly into every number in a set. For 24 and 36 it is 12. It is also called the greatest common divisor or highest common factor.

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