What is the greatest common divisor of 315 and 108?
We find the prime factorizations of the two numbers: \begin{align*}
315&=3^2\cdot5\cdot7,\\
108&=2^2\cdot3^3.
\end{align*}

The only common prime factor is $3$; the minimum exponent of $3$ is $2$, so the GCD is $3^2=\boxed{9}$.