100! 末尾有多少个 0

尾零由因子 10 贡献，等价于统计 2 与 5 的配对数；2 远多于 5，因此只需数 5 的个数：

$$\left\lfloor\frac{100}{5}\right\rfloor+\left\lfloor\frac{100}{25}\right\rfloor=20+4=24.$$

所以末尾有 24 个 0。

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Original Explanation

There are 24 trailing zeros. The number of trailing zeros equals the number of factors of 5 in $100!$ (since factors of 2 are abundant). We compute: $$\left\lfloor \frac{100}{5} \right\rfloor + \left\lfloor \frac{100}{5^2} \right\rfloor = 20 + 4 = 24.$$