Flesh out the skeleton with the number seven
The first thing to realise is that the four-digit number to be divided cannot possibly start with 2 or higher.
The first thing to realise is that the four-digit number to be divided cannot possibly start with 2 or higher. In fact, it must start with exactly 10. With this established, the remaining construction work is straightforward.
As to the bonus puzzle, the only equation where BC can appear on both sides is:
625=252