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C++ program to find factorial of large numbers

Learn: How to find factorial of large numbers in C++ using array, this program will explain finding the factorial of large number.
Submitted by Shubham Singh Rajawat, on June 05, 2017 [Last updated : February 27, 2023]

Problem statement

Given a large number, you have to write a C++ program to find its factorial.

Finding factorial of large numbers using array in C++

To find factorial of large numbers, we multiply the number from 1 to the number and every time we store the value in array from left to right for e.g. ( if I want to store 129 into the array I will store it as 921 it will be easily to do calculations this way).

• Initially 1 will be stored in the ar[] and the ar_size will also be 1
• then it will enter int the of x from x=2 to x=number multiply x*ar[]
• and update the ar[]. To store the value in ar[] following operation will take place the loop runs from i=0 to ar_size and we will store the last digit int the variable p and update the ar[] and the rest of the digits will be stored in c and in the next loop we will have to store digit by digit in ar[].

Example

Let's take an example of 5

For x=2
ar[]=1, ar_size=1
p=2*ar[]=2*1 ,c=0 
ar[]=2 ,c=0

For x=3
ar[]=2,ar_size=1
p=3*ar[]=3*2 ,c=0
ar[]=6 ,c=0

For x=4
ar[]=6,ar_size=1
p=4*ar[]=4*6=24 ,c=2
ar[]=4, c=2        ar[]=42,c=0

For x=5
ar[]=42,c=0
p=5*4=20
ar[]=0 ,c=2    
p=5*2+c=12
ar[]=021

C++ code to find factorial of large numbers using array

#include <iostream>
using namespace std;

#define size 10000

int fact(int x, int ar[], int ar_size);

void factorial(int n)
{
    int ar[size];
    ar[0] = 1;
    int ar_size = 1;

    for (int x = 2; x <= n; x++)
        ar_size = fact(x, ar, ar_size);

    for (int i = ar_size - 1; i >= 0; i--)
        cout << ar[i];

    cout << endl;
}

int fact(int x, int ar[], int ar_size)
{
    int c = 0;
    for (int i = 0; i < ar_size; i++) {
        int p = ar[i] * x + c;
        ar[i] = p % 10;
        c = p / 10;
    }

    while (c) {
        ar[ar_size] = c % 10;
        c = c / 10;
        ar_size++;
    }
    return ar_size;
}

int main()
{
    int n;

    cout << "Enter an integer number: ";
    cin >> n;

    cout << "Factorial of " << n << " is:" << endl;
    factorial(n);

    return 0;
}

Output

First run:
Enter an integer number: 20 
Factorial of 20 is: 
2432902008176640000 


Second run:
Enter an integer number: 250
Factorial of 250 is:
3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676
5272401892647332180411862610068329253651336789390895699357135301750405131787600772479330654023390061648255522488194365725860573992226412548329822048491377217766
5064127685880715312897877767295191399084437747870258917297325515028324178732065818848206247858265980884882554880000000000000000000000000000000000000000000000000
0000000000000