Greatest Common Factor Calculator
Find the GCF of two or more numbers with the work shown.
Greatest common factor
12
Least common multiple
360
Reduced by GCF
2, 3, 5
Finding the GCF
The GCF is the largest number dividing all inputs evenly. The Euclidean algorithm finds it fast: replace the larger number with the remainder of dividing it by the smaller, repeat until zero — gcd(36, 24) → gcd(24, 12) → 12.
What it's for
GCF reduces fractions to lowest terms (24/36 → 2/3), splits things into the largest equal groups, and pairs with the LCM through a tidy identity: GCF × LCM = a × b for any two numbers.
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