Two methods, same answer
Listing factors method
List every factor of each number, then pick the largest factor that appears in all lists.
Prime factorisation method
Find the prime factorisation of each number. For each prime that appears in all factorisations, take the smallest exponent. Multiply those together.
The Euclidean algorithm is a third (and the fastest) approach — see the Euclid's algorithm calculator for that.
FAQ
What's the difference between GCF, GCD and HCF?
Nothing — they're three names for the same thing. American textbooks usually say "GCF" (greatest common factor), academic / European say "GCD" (greatest common divisor), Indian say "HCF" (highest common factor).
What if the GCF is 1?
The numbers are coprime (relatively prime). They share no common factor other than 1.
How is GCF used to simplify fractions?
Divide both numerator and denominator by their GCF — that's the simplest form. e.g. 48/60: GCF(48, 60) = 12, so 48/60 = 4/5.