Solution:

Answer: 9. Note that $2007 = 3^{2} \cdot 223$. Using the fact that the number of times a prime $p$ divides $n!$ is given by
$$\left\lfloor\frac{n}{p}\right\rfloor + \left\lfloor\frac{n}{p^{2}}\right\rfloor + \left\lfloor\frac{n}{p^{3}}\right\rfloor + \cdots$$
it follows that the answer is 9.