How many zeros are there at the end of the product $10 \times 20 \times 30$ × … × 100?

Explanation

1. 01

   The product is $(10 \times 1)(10 \times 2)\dots(10 \times 10) = 10^{10} \times 10!$.

2. 02

   $10^{10}$ gives 10 zeros.

3. 03

   $10! = 3{,}628{,}800$ ends in 2 zeros (from 5 and 10).

4. 04

   Total = $10 + 2 = 12$.