Given two positive integers a and b, return their greatest common divisor (GCD) — the largest number that divides both evenly. The brute-forceBrute ForceChecking every candidate from min(a, b) down to 1, stopping at the first one that divides both numbers. approach checks candidates one at a time, which is simple but can take as many as min(a, b) steps. The Euclidean algorithmEuclidean AlgorithmRepeatedly replacing (a, b) with (b, a % b) — since any common divisor of a and b also divides a % b — until b reaches 0., one of the oldest algorithms in existence, shrinks the pair of numbers geometrically fast instead, usually finishing in a handful of rounds even for huge inputs.