Counting trailing zeros of numbers resulted from factorial

Question

I'm trying to count trailing zeros of numbers that are resulted from factorials (meaning that the numbers get quite large). Following code takes a number, compute the factorial of the number, and count the trailing zeros. However, when the number is about as large as 25!, numZeros don't work.

public static void main(String[] args) {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    double fact;
    int answer;
        
    try {
        int number = Integer.parseInt(br.readLine());
        fact = factorial(number);
        answer = numZeros(fact);
    }
    catch (NumberFormatException e) {
        e.printStackTrace();
    } catch (IOException e) {
        e.printStackTrace();
    }
}

public static double factorial (int num) {
    double total = 1;
    for (int i = 1; i <= num; i++) {
        total *= i;
    }
    return total;
}   

public static int numZeros (double num) {
    int count = 0;
    int last = 0;   

    while (last == 0) {
        last = (int) (num % 10);
        num = num / 10;
        count++;
    }
    
    return count-1;
}

I am not worrying about the efficiency of this code, and I know that there are multiple ways to make the efficiency of this code BETTER. What I'm trying to figure out is why the counting trailing zeros of numbers that are greater than 25! is not working.

Any ideas?

Answer 1

Your task is not to compute the factorial but the number of zeroes. A good solution uses the formula from http://en.wikipedia.org/wiki/Trailing_zeros (which you can try to prove)

def zeroes(n):
    i = 1
    result = 0
    while n >= i:
        i *= 5
        result += n/i  # (taking floor, just like Python or Java does)
    return result

Hope you can translate this to Java. This simply computes [n / 5] + [n / 25] + [n / 125] + [n / 625] + ... and stops when the divisor gets larger than n.

DON'T use BigIntegers. This is a bozosort. Such solutions require seconds of time for large numbers.