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Greatest Common Factor (GCF) Calculator

Compute the greatest common factor of a list of numbers, with steps.

Input Data

Numbers

Results

Greatest common factor.
6
Step-by-step derivation.
gcd(6, 18): 48=2·18+12; 18=1·12+6; 12=2·6+0 → 6 | gcd(6, 30): 6=0·30+6; 30=5·6+0 → 6
Explanatory note about the result.
GCF(48,18,30) = 6

At a glance:GCF is the GCD across a list: factor each number and take the minimum exponent per prime. Complements gcd and lcm.

Formula

GCF = gcd(gcd(...gcd(a,b),c)...).

How to Use

  1. Enter comma-separated numbers.
  2. The tool returns the GCF and steps.

Case Studies

12, 18, 24

GCF = 6.

FAQ

GCF vs GCD?

They are the same concept; GCF is the common term in schools.

Related Tools

References

Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.

Found a problem with the results?

If this calculator's result is wrong, or you have any question about the calculation logic, please let us know. You are viewing:Greatest Common Factor (GCF) Calculator（/math/gcf）。