TrailingZeroesInNFactorial

namespace TrailingZeroesInNFactorial
{
    using System;

    /// <summary>
    /// Problem 18.* Trailing Zeroes in N!
    /// Write a program that calculates with how many zeroes the factorial of a given number n has at its end.
    /// Your program should work well for very big numbers, e.g. n=100000.
    /// Examples:
    /// n   trailing zeroes of n!   explaination
    /// 10      2                   3628800
    /// 20      4                   2432902008176640000
    /// 100000  24999               think why
    /// </summary>
    public class TrailingZeroesInNFactorial
    {
        public static void Main()
        {
            Console.Write("Please enter an integer number n: ");

            int n;
            if (!int.TryParse(Console.ReadLine(), out n))
            {
                Console.WriteLine("Input was not in the correct format.");
                return;
            }

            Console.Write("{0}! --> ", n);

            // fast way - find the number of factors 5 in n! and since there are at least as much factors 2, this equivalents to the number of factors 10, each of which gives one more zero
            int zerosCount = 0;
            while (n > 0)
            {
                n = n / 5;
                zerosCount += n;
            }

            Console.WriteLine("trailing zeroes : {0}", zerosCount);
        }
    }
}