How many zeros are there at the end of 30! (the product $1 \times 2 \times 3$ × … × 30)?

Explanation

1. 01

   Each trailing zero needs a $2 \times 5$ pair, and 5s are scarcer than 2s, so count the 5s.

2. 02

   Multiples of 5 up to 30: $30 \div 5 = 6$. Multiples of 25: $30 \div 25 = 1$ (25 gives an extra 5).

3. 03

   Trailing zeros = $6 + 1 = 7$.