Cannot calculate factorials bigger than 20! ! How to do so?

Question

I am using unsigned long long integer format in order to calculate big factorials. However my code fails at some point can you have a look at it? Actually it is part of a la

Answer 1

A simple algorithm that i wrote. but it's in Java.. You can calculate factorial of 1000 in about 15 minutes.

This algorithm works with the basic formula that we learnt at primary school.

/* FOR BEST RESULT DON'T CHANGE THE CODE UNTIL YOU KNOW WHAT YOU'RE DOING */
    public String factorial(int number){
        if(number == 0) return "1";
        String result = "1";
        for(int i = 0; i < number; i++){
            result = *longNumberMultiplyingAlgorithm*(result, "" + (i + 1));
        }
        return result;  
    }

    public String longNumberMultiplyingAlgorithm(String number1, String number2){
            int maxLength = Math.max(number1.length(), number2.length());
            int a = 0;
            String[] numbers = new String[maxLength];

            if(number2.length() > number1.length()){
                String t = number1;
                number1 = number2;
                number2 = t;
            }       

            for(int i = 0; i < number1.length(); i++){
                numbers[i] = "";
                a = 0;
                for(int j = 0; j < number2.length(); j++){
                    int result = Integer.parseInt(String.valueOf(number1.charAt(number1.length() - i - 1))) * Integer.parseInt(String.valueOf(number2.charAt(number2.length() - j - 1)));
                    if(result + a < 10){
                        numbers[i] = (result + a) + "" + numbers[i];
                        a = 0;
                    }else{
                        result += a;
                        a = (int)((result + 0.0) / 10);
                        result -= a * 10;
                        numbers[i] = result + "" + numbers[i];
                    }
                }
                if(a != 0){
                    numbers[i] = a + "" + numbers[i];
                }
                for(int k = 0; k < i; k++){
                    numbers[i] += "0";
                }
            }
            return longNumberAdditionAlgorithm(numbers);
        }

    private String longNumberAdditionAlgorithm(String[] numbers) {
            String final_number = "0";
            for(int l = 0; l < numbers.length; l++){
                int maxLength = Math.max(final_number.length(), numbers[l].length());
                String number = "";
                int[] n = new int[maxLength];
                int a = 0;
                for(int i = 0; i < n.length; i++){
                    int result = 0;
                    if(i >= final_number.length()){
                        result = Integer.parseInt(String.valueOf(numbers[l].charAt(numbers[l].length() - i - 1)));
                    }else
                    if(i >= numbers[l].length()){
                        result = Integer.parseInt(String.valueOf(final_number.charAt(final_number.length() - i - 1)));
                    }else{
                        result = Integer.parseInt(String.valueOf(final_number.charAt(final_number.length() - i - 1))) + Integer.parseInt(String.valueOf(numbers[l].charAt(numbers[l].length() - i - 1)));
                    }
                    if(result + a < 10){
                        number = (result + a) + "" + number;
                        a = 0;
                    }else{
                        result -= 10;
                        number = (result + a) + "" + number;
                        a = 1;
                    }
                }
                if(a == 1){
                    number = a + "" + number;
                }
                final_number = number;
            }
            return final_number;
        }