Factorial Program in C

Last Updated : 02 May, 2025

Given a number N, the task is to find the factorial of it. A factorial is the product of all the natural numbers less than or equal to the given number N.

Examples

Input: N = 5
Output: 120
Explanation: 5! = 5 × 4 × 3 × 2 × 1 = 120
Input: N = 0
Output: 1
Explanation: 0! = 1 by definition

Find Factorial Using a Loop

The simplest way to find the factorial of a number N is by using a loop to repeatedly multiply the numbers from 1 to N and store the result in a variable.

#include <stdio.h>

unsigned int factorial(unsigned int N) {
    int fact = 1, i;

    // Loop from 1 to N to get the factorial
    for (i = 1; i <= N; i++) {
        fact *= i;
    }

    return fact;
}

int main() {
    int N = 5;
    int fact = factorial(N);
    printf("Factorial of %d is %d", N, fact);
    return 0;
}

Output

Factorial of 5 is 120

Time Complexity: O(N)
Space Complexity: O(1)

Using Recursion

The idea is to use the concept of recursion. We create a recursive function with the argument N which will progressively decrement by 1 till it reaches 0. In each recursive call, we return the function call for decremented N after multiplying it with current N. At the end, we will be left with the factorial of N.

#include <stdio.h>

unsigned int factorial(unsigned int n) {
  
    // Base Case:
    if (n == 1) {
        return 1;
    }

    // Multiplying the current N with the previous product
    // of Ns
    return n * factorial(n - 1);
}

int main() {
    int num = 5;
    printf("Factorial of %d is %d", num, factorial(num));
    return 0;
}

Output

Factorial of 5 is 120

Time Complexity: O(N)
Auxiliary Space: O(N), due to the recursive call stack.

Using Arrays (for Large Numbers)

Factorial may get very large which can be troublesome because the largest number the C++ is 18,446,744,073,709,551,615. We can solve this using strings to store the numbers and perform the multiplication.

Convert the given number N to the string num.
Multiply the num with every number from 1 to N with the current value stored in the array fact. Refer this article to know about it.
Print the digits of the result array in reverse order.

#include <stdio.h>
#include <string.h>

// Function to multiply a string (representing a number)
// by an integer
void multiplyString(char num[], int factor) {
    int len = strlen(num);
    int carry = 0;

    for (int i = len - 1; i >= 0; i--) {
        int digit = num[i] - '0';
        int product = digit * factor + carry;
        num[i] = (product % 10) + '0';
        carry = product / 10;
    }

    // Handling the carry by adding digits to the front
  	// of the number
    while (carry) {
        for (int i = strlen(num); i >= 0; i--) {
            num[i + 1] = num[i];
        }
        num[0] = (carry % 10) + '0';
        carry /= 10;
    }
}

// Function to find factorial using a string
void factorialString(int N) {
  
    // Use a large enough buffer
    char fact[1000];
  
    // Initialize result as "1"
    strcpy(fact, "1");

    for (int i = 2; i <= N; i++) {
      
        // Multiply the string in each iteration
        multiplyString(fact, i);
    }

    printf("Factorial of %d is %s", N, fact);
}

int main() {
    int N = 5;
    factorialString(N);
    return 0;
}

Output

Factorial of 5 is 120

Time Complexity: O(N log²N)
Auxiliary Space: O(logN)

C/C++ Programs

kartik

Improve

Article Tags :

Practice Tags :

factorial

Factorial Program in C

Find Factorial Using a Loop

Using Recursion

Using Arrays (for Large Numbers)

Related Articles:

Similar Reads

Thank You!

What kind of Experience do you want to share?