Dynamic Programming21 sections · 915 units
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GCD - Recursive Formula

The Euclidean algorithm

The complete recursive formula is: gcd⁡(a,b)={aif b=0gcd⁡(b,a mod b)otherwise\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 300300 BCE. It is one of the oldest algorithms still used today.

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