Factorial of a Number in C++

Factorial in C++: 5! is 120. Use long long — 13! overflows int. 0! is 1.

BeginnerLoop ProgramsExample 3 of 14

factorial-of-a-number.cpp

1#include <iostream>
2using namespace std;
3
4int main() {
5    int n;
6    long long factorial = 1;
7    
8    cout << "Enter a positive integer: ";
9    cin >> n;
10    
11    if (n < 0) {
12        cout << "Factorial is not defined for negative numbers" << endl;
13    } else {
14        for (int i = 1; i <= n; i++) {
15            factorial *= i;
16        }
17        cout << "Factorial of " << n << " = " << factorial << endl;
18    }
19    
20    return 0;
21}

Output

Enter a positive integer: 5
Factorial of 5 = 120

What's going on

n! in C++ is 1 × 2 × … × n. 5! is 120. That's the sample. 0! is 1. Negative n is not defined.

int n;

long long factorial = 1;

Start the product at 1, not 0. 0 * anything is 0, and you never recover.

Why long long: 13! is 6,227,020,800. That does not fit in a 32-bit int (~2.1 billion). long long holds through 20!. 21! overflows even that.

cin >> n;

Sample: 5.

if (n < 0)

Print that factorial isn't defined. Don't run the loop on -3.

for (int i = 1; i <= n; i++)

factorial *= i; (same as factorial = factorial * i)

Walk 5:

start 1

×1 → 1

×2 → 2

×3 → 6

×4 → 24

×5 → 120

n == 0: the loop condition 1 <= 0 is false. factorial stays 1. That's 0!.

n == 1: one iteration, still 1.

Then cout << "Factorial of " << n << " = " << factorial. Sample: Factorial of 5 = 120.

A recursive fact(n) = n * fact(n-1) is the same math with a stack. Missing the n <= 1 base case is a crash, not a clever answer.

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