GCF Calculator
Enter two or more numbers and get the GCF instantly. Everything runs on your device - nothing is ever uploaded.
Runs entirely on your device - nothing is ever uploaded.
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How to use the GCF Calculator
- Type two or more whole numbers, separated by commas.
- Read the greatest common factor - the largest number dividing every input evenly.
- Use it to reduce a fraction or factor an expression.
What it is for
Reducing fractions to lowest terms, factoring expressions, and splitting quantities into the largest equal groups. Packing 48 apples and 180 oranges into identical boxes means boxes of 12 - the GCF - with nothing left over.
How it works
The GCF comes from the Euclidean algorithm, folding across every number you enter; the LCM is built from the same factors. Both are exact for any whole numbers up to 15 digits.
What is the greatest common factor
The GCF is the largest number that divides every input evenly. For 48 and 180, Euclid's algorithm repeatedly replaces the pair with the remainder: 180 ÷ 48 leaves 36, 48 ÷ 36 leaves 12, 36 ÷ 12 leaves 0, so the GCF is 12. Equivalently, 48 = 2⁴ × 3 and 180 = 2² × 3² × 5, and the GCF takes each shared prime at its lowest power: 2² × 3 = 12.
Reducing fractions with the GCF
The everyday use of the GCF is simplifying fractions: divide top and bottom by it. Since GCF(48, 180) = 12, the fraction 48/180 reduces to 4/15 in one step. It also factors expressions - pulling 12x + 18 apart starts with GCF(12, 18) = 6, giving 6(2x + 3).