GCD - Problem Statement

Given two positive integers $a$ and $b$, find their greatest common divisor (GCD), the largest number that divides both. For example, $\gcd(48, 18) = 6$ because $6$ divides both $48$ and $18$, and no larger number does.

You could try every number from $1$ to $\min(a, b)$ and check which ones divide both. That works but is slow. There is a recursive solution that is clean and fast. Before reading on, think: what relationship might exist between $\gcd(a, b)$ and smaller inputs?