1977 AMC 12 第 25 题

Count the factors of $5$ in $1005!$

Include contributions from multiples of $25,$ $125,$ and $625$

There are more factors of $2$ than of $5,$ so the exponent of $10$ is $$\begin{aligned} n={}&\left\lfloor\frac{1005}{5}\right\rfloor+ \left\lfloor\frac{1005}{25}\right\rfloor\\ &+\left\lfloor\frac{1005}{125}\right\rfloor+ \left\lfloor\frac{1005}{625}\right\rfloor\\ ={}&201+40+8+1=250. \end{aligned}$$ Since $250$ is not listed, the correct choice is “none of these.”

Therefore, the correct answer is E.