6.11Loops_TrailingZeroesInNFactorials

// 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.

namespace _18.TrailingZeroesInN_Factorial
{
    using System;
    using System.Numerics;

    public class TrailingZeroesInN_Factorial
    {
        public static void Main(string[] args)
        {
            checked
            {
                int numN;
                do
                {
                    Console.Write("Enter a positive Integer number: ");
                }
                while (!int.TryParse(Console.ReadLine(), out numN) || numN < 1);

                // Just in case we'll calculate and N!:
                BigInteger factorialN = 1;
                for (int i = numN; i > 1; i--)
                {
                    factorialN *= i;
                }

                // Calculate count of Zeroes in N!, without calculating N! him self:
                int countZeroes = 0;
                int quotient = numN;
                do
                {
                    quotient /= 5;
                    countZeroes += quotient;
                }
                while (quotient > 1);

                Console.WriteLine("Factorial of number {0} is: {1}\n", numN, factorialN);
                Console.WriteLine("Trailing Zeroes in {0}! is: {1} !", numN, countZeroes);
            }
        }
    }
}