Number theory

Greatest Common Factor Calculator

Calculate the largest positive integer that divides all entered numbers.

Why GCF matters

GCF is the number used to reduce fractions, simplify ratios and find the largest equal group size that divides several quantities.

Example

For 24, 36 and 60, the greatest common factor is 12 because 12 divides all three numbers and no larger positive integer does.

GCF vs LCM

Use GCF when simplifying or splitting into equal groups. Use least common multiple when finding a common denominator or when repeating cycles need to line up.

Common mistakes

Do not confuse common factors with common multiples. Factors divide into the numbers; multiples are produced by multiplying them.

Last reviewed: 2026-05-17

Before relying on this result

Use this calculator together with the formula, assumptions, limitations and examples on the page. If the topic involves health, tax, lending, investment, legal, safety or current-rate decisions, treat the number as an estimate and check the relevant primary source or professional guidance.

Calculator metadata last reviewed: 2026-05-14.