# Write a C program to find out the Factorial of a Given Number ?

#include

```
#include
void main()
{
int n,i,fact=1;
clrscr();
printf(“enter the number
```

”);

```
scanf(“%d”,&n);
for(i=n;i>=1;i--)
{
fact=fact*i;
}
printf(“the factorial of given number is %d”,fact);
getch();
}
Output:
enter the number
5
the factorial of given number is 120
```

Recursion: A function is called ‘recursive’ if a statement within the body of a function calls the same

function. It is also called ‘circular definition’. Recursion is thus a process of defining something in terms of itself. Program: To calculate the factorial value using recursion.

#include

int fact(int n);

int main() {

int x, i;

printf("Enter a value for x:

");

scanf("%d", &x);

i = fact(x);

printf("

Factorial of %d is %d", x, i);

return 0;

} int fact(int n) {

/* n=0 indicates a terminating condition */

if (n <= 0) {

return (1);

} else {

/* function calling itself */

return (n * fact(n - 1));

/*n*fact(n-1) is a recursive expression */

}

}

Output:

Enter a value for x:

4

Factorial of 4 is 24

Explanation:

fact(n) = n * fact(n-1)

If n=4

fact(4) = 4 * fact(3) there is a call to fact(3)

fact(3) = 3 * fact(2)

fact(2) = 2 * fact(1)

fact(1) = 1 * fact(0)

fact(0) = 1

fact(1) = 1 * 1 = 1

fact(2) = 2 * 1 = 2

fact(3) = 3 * 2 = 6

Thus fact(4) = 4 * 6 = 24

Terminating condition(n <= 0 here;) is a must for a recursive program. Otherwise the program enters

into an infinite loop.