Number theory

Common Factor Calculator

Find the positive factors shared by two numbers.

When common factors help

Common factors are useful for simplifying fractions, comparing ratios and splitting quantities into equal groups. If two numbers share a factor, both numbers can be divided by that factor without leaving a remainder.

Example

For 36 and 60, the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18 and 36. The factors of 60 include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. The shared factors are 1, 2, 3, 4, 6 and 12, so the greatest common factor is 12.

Common mistakes

Do not confuse a common factor with a common multiple. A factor divides into a number; a multiple is the result of multiplying a number. For fraction simplification, use the greatest common factor to reduce both numerator and denominator by the same amount.

Limitations

This calculator is intended for whole-number factor comparisons. Decimal values, algebraic expressions and very large integers may need a different method.

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.