What this calculator does
The greatest common factor (GCF), also called the greatest common divisor (GCD), is the largest whole number that divides two given numbers with no remainder. It is a core building block for simplifying fractions and reducing ratios to their lowest terms.
How the GCF is calculated
This calculator uses the Euclidean algorithm: repeatedly divide the larger number by the smaller one and replace the larger number with the remainder, until the remainder reaches zero. Whatever number is left is the GCF. It also reports the least common multiple (LCM), which is related to the GCF by LCM(a, b) = (a × b) ÷ GCF(a, b).
Good to know
Enter whole numbers only; decimal inputs are rounded automatically. This tool is intended for general educational and homework-checking purposes.
Last reviewed August 2026