GCF Calculator
Find the greatest common factor of two numbers instantly.
Find the greatest common factor (GCF, also called GCD) of two numbers — the largest number that divides both evenly. Used for simplifying fractions and ratios, factoring expressions, and splitting quantities into equal groups.
How it's calculated
The GCF is found with the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller until the remainder is zero — the last non-zero remainder is the GCF.
Frequently asked questions
What is the GCF of 12 and 18?
6. It's the largest number that divides both 12 and 18 evenly.
What is the difference between GCF and GCD?
Nothing — GCF (greatest common factor) and GCD (greatest common divisor) are two names for the same thing.
How is the GCF used to simplify fractions?
Divide the numerator and denominator by their GCF. For 12/18, the GCF is 6, so 12/18 simplifies to 2/3.