An integer $latex x $ has $latex n $ zeros at the end if and only if it is divisible by $latex 10^n $. For example, 12,500,000 is divisible by $latex 10^5 $ but not by $latex 10^6 $.

How many zeros are at the end of $latex 1 \times 2 \times 3 \times \cdots \times 100$?

1. 1 (check answer)
2. 3 (check answer)
3. 10 (check answer)
4. 20 (check answer)
5. 24 (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 12th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.