Trailing zeros of 100 factorial

How many zeros does $100!$ end in?

24. Each trailing zero needs a factor $10=2\cdot5$, and factors of $5$ are scarcer. Multiples of $5$ up to $100$ contribute $20$, and multiples of $25$ contribute $4$ more, for $\lfloor100/5\rfloor+\lfloor100/25\rfloor=24$.