Supose $\displaystyle a,b,c$ are positive integers so that $\displaystyle a+b+c=2010$ and $\displaystyle a!*b!*c!=m*10^n$ where $\displaystyle m$ and $\displaystyle n$ are integers and $\displaystyle m$ is not divisible by 10. Which is the minimum value $\displaystyle n$ can have?

The first thing I did was to find the values a,b,c should have to minimize the multiplication of factorials. Dividing 2010 by 3 = 670, then a=669, b=670 and c=671. Now I stuck, can someone help?