smc

The power of $10$ for any factorial is given by the well-known algorithm $$\lfloor \frac{n}{5}\rfloor +\lfloor \frac{n}{25}\rfloor +\lfloor \frac{n}{125}\rfloor +\cdots$$ It is rational to guess numbers right before powers of $5$ because we won't have any extra numbers from higher powers of $5$. As we list out the powers of 5, it is clear that $5^4=625$ is less than 2006 and $5^5=3125$ is greater. Therefore, set $a$ and $b$ to be 624. Thus, c is $2006-(624\cdot 2)=758$. Applying the algorithm, we see that our answer is $152+152+188=\boxed{492}$.