Definition: The largest integer that divides all inputs without remainder.
Euclidean Algorithm (fast):
repeatedly compute a = b, b = a mod b until b = 0. Last non-zero b is the GCF.
Prime factor method (small numbers):
factor each integer and multiply the primes that appear in every factorization with the smallest exponents.
Signs & zeros: negatives are treated by absolute value; gcf(0, n) = |n|; all zeros is undefined.
Co-prime: if GCF = 1, numbers are relatively prime.
Reduction: dividing each number by the GCF yields the simplest integer ratio.
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