I'm bored with life

You are given two positive integers $a$ and $b$.

Consider all possible pairs $(x, y)$ such that:

• $x$ is a positive divisor of $a$,
• $y$ is a positive divisor of $b$.

For every such pair, compute $\gcd(x, y)$. Your task is to output the maximum value that can be obtained.

Intuition

The answer depends only on the greatest common divisor of the two numbers, because any common divisor of $a$ and $b$ can be chosen as a divisor of each.