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.

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