C Program to Find Factorial of a Number

A C program to find factorial of a number uses a loop to multiply all integers from 1 to that number, like for(int i=1; i<=n; i++) factorial *= i;.

Examples

Input0

OutputFactorial of 0 is 1

Input5

OutputFactorial of 5 is 120

Input10

OutputFactorial of 10 is 3628800

How to Think About It

To find the factorial of a number, think of multiplying all whole numbers from 1 up to that number. Start with 1, then multiply by 2, then 3, and so on until you reach the number. This gives the total product called factorial.

Algorithm

1

Get input number from the user

2

Initialize a variable factorial to 1

3

Loop from 1 to the input number

4

Multiply factorial by the current loop number each time

5

After the loop ends, print the factorial value

Code

c

#include <stdio.h>

int main() {
    int n, factorial = 1;
    printf("Enter a number: ");
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        factorial *= i;
    }
    printf("Factorial of %d is %d\n", n, factorial);
    return 0;
}

Output

Enter a number: 5
Factorial of 5 is 120

Dry Run

Let's trace the input 5 through the code

1

Input

User enters 5, so n = 5

2

Initialize factorial

factorial = 1

3

Loop start

i = 1, factorial = 1 * 1 = 1

4

Loop iteration 2

i = 2, factorial = 1 * 2 = 2

5

Loop iteration 3

i = 3, factorial = 2 * 3 = 6

6

Loop iteration 4

i = 4, factorial = 6 * 4 = 24

7

Loop iteration 5

i = 5, factorial = 24 * 5 = 120

8

Loop ends

Loop ends as i > n

9

Output

Print 'Factorial of 5 is 120'

i	factorial
1	1
2	2
3	6
4	24
5	120

Why This Works

Step 1: Initialize factorial

We start with factorial = 1 because multiplying by 1 does not change the value and it is the identity for multiplication.

Step 2: Multiply in loop

Each loop multiplies factorial by the current number i, building the product step by step.

Step 3: Final result

After the loop finishes, factorial holds the product of all numbers from 1 to n, which is the factorial.

Alternative Approaches

Recursive function

c

#include <stdio.h>

int factorial(int n) {
    if (n <= 1) return 1;
    else return n * factorial(n - 1);
}

int main() {
    int n;
    printf("Enter a number: ");
    scanf("%d", &n);
    printf("Factorial of %d is %d\n", n, factorial(n));
    return 0;
}

Uses function calling itself; elegant but uses more memory due to call stack.

Using while loop

c

#include <stdio.h>

int main() {
    int n, factorial = 1, i = 1;
    printf("Enter a number: ");
    scanf("%d", &n);
    while (i <= n) {
        factorial *= i;
        i++;
    }
    printf("Factorial of %d is %d\n", n, factorial);
    return 0;
}

Uses while loop instead of for; same logic but different loop style.

Complexity: O(n) time, O(1) space

Time Complexity

The program runs a single loop from 1 to n, so it takes linear time proportional to n.

Space Complexity

Only a few variables are used, so space is constant regardless of input size.

Which Approach is Fastest?

Both iterative and recursive methods have O(n) time, but iterative uses less memory and is generally faster.

Approach	Time	Space	Best For
Iterative for loop	O(n)	O(1)	Simple and efficient for all inputs
Recursive function	O(n)	O(n)	Clear logic but uses more memory
While loop	O(n)	O(1)	Same as for loop, just different syntax