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.