Gcf/gcd Calculator
Greatest Common Factor works out Greatest common factor and Least common multiple from Numbers and Maximum factors to list. The default figures on this page give greatest common factor of 6; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
5 steps
- 12 = 2^2 x 3
- 18 = 2 x 3^2
- GCF = the product of every prime raised to its lowest shared power = 6.
- LCM = the product of every prime raised to its highest power = 36.
- Check: GCF x LCM = 6 x 36 = 216, which equals 12 x 18.
All common factorstable
Prime factorizationstable
numbersUsedtable
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Greatest Common Factor calculates
Finds the greatest common factor (GCD/HCF) and least common multiple of two or more whole numbers, with the Euclidean, prime-factorization or factor-listing working shown.
How to use this Greatest Common Factor
Enter Numbers and Maximum factors to list. Greatest common factor updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Greatest common factor, Least common multiple and GCF (exact).
The method follows Euclid, Elements, Book VII, Propositions 1-3 (the Euclidean algorithm), NIST Digital Library of Mathematical Functions, §27.1-27.2 (divisibility, fundamental theorem of arithmetic) and Common Core State Standards for Mathematics, 6.NS.B.4 (greatest common factor and least common multiple).
What you can compare
Change one input at a time to see how it affects Greatest common factor, Least common multiple and GCF (exact). The inputs you can vary are Numbers and Maximum factors to list.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
Can you do GCF on a calculator?
Finds the greatest common factor (GCD/HCF) and least common multiple of two or more whole numbers, with the Euclidean, prime-factorization or factor-listing working shown. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give 6.
What's the easiest way to calculate the GCF?
Finds the greatest common factor (GCD/HCF) and least common multiple of two or more whole numbers, with the Euclidean, prime-factorization or factor-listing working shown. Open “How this is worked out” beside the result to see each step for your own figures.
How to find GCF on a TI-84 calculator?
It needs Numbers and Maximum factors to list. Nothing else is required, and the figures stay in your browser.
How to easily calculate GCF?
The result gives Greatest common factor, Least common multiple, GCF (exact), LCM (exact), All common factors and Prime factorizations, each labelled with its unit so the figure can be read on its own.
What information do I need for the Greatest Common Factor?
You need Numbers and Maximum factors to list. The page opens with default figures that give greatest common factor of 6, so you can see the scale before entering your own.
What does this Greatest Common Factor show?
It shows Greatest common factor, Least common multiple, GCF (exact), LCM (exact), All common factors, Prime factorizations, Numbers are coprime and GCF x LCM (two numbers only), with the working and any warnings for your entries.