Solution
= Solution
{c}
The successive <division with remainder> steps of the <Euclidean algorithm> are
$$
\begin{aligned}
657&=2\cdot306+45,\\
306&=6\cdot45+36,\\
45&=1\cdot36+9,\\
36&=4\cdot9+0.
\end{aligned}
$$
Each step preserves the <greatest common divisor> by part (a). The final nonzero <remainder> is $9$, so
$$
\boxed{\gcd(306,657)=9.}
$$