Why computing factorial of realtively small numbers (34+) returns 0

Question

int n = Convert.ToInt32(Console.ReadLine());
int factorial = 1;

for (int i = 1; i <= n; i++)
{
    factorial *= i;    
}
Console.WriteLine(factorial);

This code runs in Console Application, but when a number is above 34 application returns 0.

Why 0 is returned and what can be done to compute factorial of large numbers?

Answer 1

You're going out of range of what the variable can store. That's effectively a factorial, which grows faster than the exponential. Try using ulong (max value 2^64 = 18,446,744,073,709,551,615) instead of int (max value 2^31 = 2,147,483,647) - ulong p = 1 - that should get you a bit further.

If you need to go even further, .NET 4 and up has BigInteger, which can store arbitrarily large numbers.

Answer 2

You are getting 0 because of the way integer overflow handled in most programming languages. You can easily see what happens if you output results of each computation in a loop (using HEX representation):

int n = Convert.ToInt32(Console.ReadLine());
int factorial = 1;
for (int i = 1; i <= n; i++)
{
  factorial *= i;
  Console.WriteLine("{0:x}", factorial);
}
Console.WriteLine(factorial);

For n = 34 result look like:

1 2 6 18 78 2d0 13b0 ... 2c000000 80000000 80000000 0

Basically multiplying by 2 shifts numbers left and when you multiplied numberer containing enough twos all significant digits will fall out of integer which is 32 bits wide (i.e. first 6 numbers give you 4 twos : 1, 2, 3, 2*2, 5, 2*3, so result of multipying them is 0x2d0 with 4 zero bits at the end).

Answer 3

If you are using .net 4.0 and want to calculate factorial of 1000, then try to use BigInteger instead of Int32 or Int64 or even UInt64. Your problem statement "doesn't work" is not quite sufficient for me to give some good subjection. Your code will look something like:

using System;
using System.Numerics;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main()
        {
            int factorial = Convert.ToInt32(Console.ReadLine());

            var result = CalculateFactorial(factorial);

            Console.WriteLine(result);
            Console.ReadLine();
        }

        private static BigInteger CalculateFactorial(int value)
        {
            BigInteger result = new BigInteger(1);
            for (int i = 1; i <= value; i++)
            {
                result *= i;
            }
            return result;
        }
    }
}