# Factorial of a large number

Data StructureMisc AlgorithmsAlgorithms

In computers, variables are stored in memory locations. But the size of the memory location is fixed, so when we try to find the factorial of some greater value like 15! or 20! the factorial value exceeds the memory range and returns wrong results.

For calculation of large numbers, we have to use an array to store results. In each element of the array, is storing different digits of the result. But here we cannot multiply some number with the array directly, we have to perform manual multiplication process for all digits of the result array.

## Input and Output

Input:
A big number: 50
Output:
Factorial of given number is:
30414093201713378043612608166064768844377641568960512000000000000

## Algorithm

multiply(x, multiplicand)

Input: The number x, and the large multiplicand as an array.

Output: Result after multiplication.

Begin
carry := 0
for all digits i of multiplicand, do
prod := i*x+carry
i := prod mod 10
carry := prod / 10
done

while carry ≠ 0, do
insert (carry mod 10) at the end of multiplicand array
carry := carry/10
done
End

factorial(n)

Input: The number n.

Output: Find factorial of n.

Begin
define result array.
insert 1 in the result

for i := 2 to n, do
multiply(i, result)
done

reverse the result
return result
End

## Example

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;

void multiply(int x, vector<int>&multiplicand) {    //multiply multiplicand with x
int carry = 0;     // Initialize carry to 0
vector<int>::iterator i;

for (i=multiplicand.begin(); i!=multiplicand.end(); i++) {   //multiply x with all digit of multiplicand
int prod = (*i) * x + carry;
*i = prod % 10;       //put only the last digit of product
carry  = prod/10;    //add remaining part with carry
}

while (carry) {    //when carry is present
multiplicand.push_back(carry%10);
carry = carry/10;
}
}

void factorial(int n) {
vector<int> result;
result.push_back(1);    //at first store 1 as result

for (int i=2; i<=n; i++)
multiply(i, result);   //multiply numbers 1*2*3*......*n

cout << "Factorial of given number is: "<<endl;

reverse(result.begin(), result.end());

vector<int>::iterator it;    //reverse the order of result

for(it = result.begin(); it != result.end(); it++)
cout << *it;
}

int main() {
factorial(50);
}

## Output

Factorial of given number is:
30414093201713378043612608166064768844377641568960512000000000000