Factors & Multiples · Superchallenge problem

The Euclidean algorithm on $(2026, b)$ divides $2026$ by $b$; if the remainder $r$ is not $0$ it then divides $b$ by $r$, and so on, stopping at the first remainder $0$. For how many integers $b$ with $1 \le b \le 2026$ does the algorithm stop after EXACTLY two divisions?