This C program is used to calculate the factorial value using recursion.

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.

Program:

```
#include <stdio.h>
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
}
}
```

Program 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.