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GCF Calculator

Greatest common factor, with every common factor listed.

Work out GCF. Greatest common factor, with every common factor listed. Handles the cases the shortcuts get wrong.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Optional.

Optional.

Greatest common factor

6

Simplifies to 2 : 3

Numbers12, 18
Greatest common factor6
Lowest common multiple36
All common factors1, 2, 3, 6
Simplified ratio2 : 3
CoprimeNo

The GCF and LCM are linked: for two numbers, GCF × LCM equals the product of the numbers themselves. Here 6 × 36 accounts for every prime factor exactly once between them — the GCF taking the shared ones and the LCM the union.

How the GCF Calculator works

The greatest common factor of two or more numbers, found by the Euclidean algorithm. It also lists every common factor rather than just the largest, and shows the simplified ratio the GCF produces — which is what the GCF is usually wanted for.

Also known as: greatest common factor · gcd calculator · highest common factor calculator · hcf calculator

Frequently asked questions

How do I find the greatest common factor?

Repeatedly replace the larger number with its remainder against the smaller until one reaches zero. For 48 and 18 this gives 6 in three steps, far faster than listing factors.

What is the difference between GCF, GCD and HCF?

Nothing — greatest common factor, greatest common divisor and highest common factor are three names for the same quantity.

What does it mean if the GCF is 1?

The numbers are coprime: they share no factor above 1. Any ratio between them is already in lowest terms.

How is the GCF related to the LCM?

For two numbers, GCF × LCM equals their product. The GCF takes the shared prime factors and the LCM takes the union of them.

Put this calculator on your own site

Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.

The one-line version
<iframe src="https://www.thecalclibrary.com/embed/gcf-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="GCF Calculator"></iframe>

The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.

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