C++ Program to Find Factorial of a Number

You can find the factorial of a number in C++ by using a loop that multiplies numbers from 1 to the given number, like for (int i = 1; i <= n; ++i) result *= 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, multiply all whole numbers from 1 up to that number. If the number is 0, the factorial is 1 by definition. Use a loop to multiply these numbers step by step.

Algorithm

1

Get the input number from the user

2

If the number is 0, return 1 as factorial

3

Initialize a variable to 1 to store the result

4

Loop from 1 to the input number

5

Multiply the result by the current loop number each time

6

After the loop ends, return the result

Code

cpp

#include <iostream>
using namespace std;

int main() {
    int n;
    unsigned long long factorial = 1;
    cout << "Enter a positive integer: ";
    cin >> n;
    if (n < 0) {
        cout << "Factorial is not defined for negative numbers." << endl;
        return 1;
    }
    for (int i = 1; i <= n; ++i) {
        factorial *= i;
    }
    cout << "Factorial of " << n << " is " << factorial << endl;
    return 0;
}

Output

Enter a positive integer: 5
Factorial of 5 is 120

Dry Run

Let's trace the input 5 through the code

1

Input

User enters n = 5

2

Initialize factorial

factorial = 1

3

Loop iteration 1

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

End loop

factorial = 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 result and it is the identity for multiplication.

Step 2: Multiply in loop

Each loop step multiplies factorial by the current number i, building the product of all numbers from 1 to n.

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

cpp

#include <iostream>
using namespace std;

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

int main() {
    int n;
    cout << "Enter a positive integer: ";
    cin >> n;
    if (n < 0) {
        cout << "Factorial is not defined for negative numbers." << endl;
        return 1;
    }
    cout << "Factorial of " << n << " is " << factorial(n) << endl;
    return 0;
}

Uses recursion which is elegant but can cause stack overflow for very large n.

Using while loop

cpp

#include <iostream>
using namespace std;

int main() {
    int n;
    unsigned long long factorial = 1;
    cout << "Enter a positive integer: ";
    cin >> n;
    if (n < 0) {
        cout << "Factorial is not defined for negative numbers." << endl;
        return 1;
    }
    int i = 1;
    while (i <= n) {
        factorial *= i;
        i++;
    }
    cout << "Factorial of " << n << " is " << factorial << endl;
    return 0;
}

Uses a while loop instead of for loop, functionally the same but different style.

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

Time Complexity

The program multiplies numbers from 1 to n once, so it runs in linear time O(n).

Space Complexity

Only a few variables are used, so space is constant O(1).

Which Approach is Fastest?

The iterative for loop is fastest and safest for large n compared to recursion which can cause stack overflow.

Approach	Time	Space	Best For
Iterative for loop	O(n)	O(1)	Large inputs, safe and fast
Recursive function	O(n)	O(n)	Simple code, small inputs
While loop	O(n)	O(1)	Same as for loop, style preference