GCD - Recursive Formula

The complete recursive formula is: $\gcd(a, b) = \begin{cases} a & \text{if } b = 0 \\ \gcd(b, a \bmod b) & \text{otherwise} \end{cases}$ This is the Euclidean algorithm, invented around $300$ BCE. It is one of the oldest algorithms still used today.

Notice how each call swaps the arguments: $a$ becomes $b$, and $b$ becomes $a \bmod b$. This is your first recursion with two changing parameters. Each recursive call brings you closer to the base case.