GCF Calculator
Find the Greatest Common Factor (GCF), also called GCD, of two or more numbers.
About the GCF Calculator
The Greatest Common Factor — also called the greatest common divisor — is the largest number that divides evenly into every number in a set, used constantly for simplifying fractions and factoring expressions. This calculator finds the GCF of any list of numbers.
How It Works
The calculator applies the Euclidean algorithm, a highly efficient method that repeatedly replaces the larger of two numbers with the remainder of dividing it by the smaller, until the remainder reaches zero — the last nonzero remainder is the greatest common factor. It applies this pairwise across the full list.
GCD(a,b): repeatedly replace (a,b) with (b, a mod b) until b = 0; the last nonzero a is the GCF. Applied iteratively across all numbers.
Example
Scenario: Finding the GCF of 24, 36, and 60.
Result: The GCF is 12, the largest number that divides evenly into 24, 36, and 60.
Assumptions & Limitations
- Requires at least two numbers to compute a meaningful greatest common factor.
- Works with positive whole numbers, consistent with the standard mathematical definition of GCF.
- If the numbers share no common factor other than 1, the GCF will correctly be reported as 1.