在不计算阶乘Java的情况下从大量数字中查找阶乘尾零

Question

一些被测试的数字将导致10000位的阶乘，因此计算这一数字以找到尾随的零似乎是不可能的。如何在不计算阶乘的情况下找到尾随零的数量。

        long sum = 1;
        for (int i = 1; i < n+1; i++) {
            sum *= i;
        }
        char[] length = String.valueOf(sum).toCharArray();
        int count = 0;
        for (int i = length.length-1; i > 0; i--) {
                if (length[i] == '0')
                    count++;
                if (length[i] != '0')
                    break;
        }
        return count;
    }

Answer 1

我确实相信解决方案是（不包括整数溢出）：

public static int zerosFactorialTrailing(int n) {
    int fives = 0;
    for (int i = 5; i <= n; i *= 5) {
        fives += n / i;
    }
    /*
     * There are always more twos than fives
     *
    int twos = 0;
    for (int i = 2; i <= n; i *= 2) {
        twos += n / i;
    }
    return Math.min(twos, fives);
    */
    return fives;
}