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Greatest Common Factor Calculator
Divisor Forge
GCF & LCM Multi-Factor Processor
About the Greatest Common Factor Calculator
The greatest common factor (GCF), also called the greatest common divisor, is the largest number that divides every number in a set exactly. It is used to simplify fractions and split things into equal groups.
How to use the Greatest Common Factor Calculator
- Enter your integers in Integer Set, separated by commas.
- Press Calculate to see the GCF and the steps.
Formula and method
The calculator uses the Euclidean algorithm: gcd(a, b) = gcd(b, a mod b), repeated until the remainder is zero. For more than two numbers it applies the method pair by pair.
Worked example
For 24, 36 and 48 the GCF is 12, because 12 divides all three and no larger number does.
Tips
- To simplify a fraction, divide numerator and denominator by their GCF.
- If the GCF is 1, the numbers are called coprime.
Frequently Asked Questions
The GCF is the largest number that divides all the numbers. The LCM is the smallest number that all of them divide into.