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Factorial of a non-negative integer n is the product of all the positive integers that are less than or equal to n.

For example: The factorial of 5 is 120.

5! = 5 * 4 * 3 * 2 *1 5! = 120

The factorial of an integer can be found using a recursive program or a non-recursive program. Example of both of these are given as follows.

A for loop can be used to find the factorial of a number. This is demonstrated using the following program −

#include <iostream> using namespace std; int main() { int n = 5, fact = 1, i; for(i=1; i<=n; i++) fact = fact * i; cout<<"Factorial of "<<n<<" is "<<fact; return 0; }

Factorial of 5 is 120

In the above program, the for loop runs from 1 to n. For each iteration of the loop, fact is multiplied with i. The final value of fact is the product of all numbers from 1 to n. This is demonstrated using the following code snippet.

for(i=1; i<=n; i++) fact = fact * i;

The following program demonstrates a recursive program to find the factorial of a number.

#include <iostream> using namespace std; int fact(int n) { if ((n==0)||(n==1)) return 1; else return n*fact(n-1); } int main() { int n = 5; cout<<"Factorial of "<<n<<" is "<<fact(n); return 0; }

Factorial of 5 is 120

In the above program, the function fact() is a recursive function. The main() function calls fact() using the number whose factorial is required. This is demonstrated by the following code snippet.

cout<<"Factorial of "<<n<<" is "<<fact(n);

If the number is 0 or 1, then fact() returns 1. If the number is any other, then fact() recursively calls itself with the value n-1.

This is demonstrated using the following code snippet −

int fact(int n) { if ((n==0)||(n==1)) return 1; else return n*fact(n-1); }

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