What is the remainder when 12! is divided by 13?

Wilson's theorem says that for a prime $p$, the factorial $(p-1)$! leaves remainder $p-1$ on division by $p$. Here $p=13$, so 12! leaves 12. Checking directly, 12! = 479001600 and $13\times 36846276=479001588$, a difference of 12. The trap is 0: a factorial is a multiple of everything up to itself, but 12! never picks up the factor 13, so it is not a multiple of 13.