**Factorial Program in C using Recursion**

A recursive approach to finding the factorial involves calling the function itself with a reduced problem size. Here's the code:

```
#include <stdio.h>
unsigned long long factorial(unsigned int n) {
if (n == 0) {
return 1;
} else {
return n * factorial(n - 1);
}
}
int main() {
unsigned int n;
printf("Enter a number: ");
scanf("%u", &n);
printf("Factorial of %u is %llu\n", n, factorial(n));
return 0;
}
```

### Using Tail Recursion

Tail recursion optimizes recursive functions by reducing the amount of memory used. Here's the factorial code with tail recursion:

```
#include <stdio.h>
unsigned long long factorial_helper(unsigned int n, unsigned long long acc) {
if (n == 0) {
return acc;
} else {
return factorial_helper(n - 1, acc * n);
}
}
unsigned long long factorial(unsigned int n) {
return factorial_helper(n, 1);
}
int main() {
unsigned int n;
printf("Enter a number: ");
scanf("%u", &n);
printf("Factorial of %u is %llu\n", n, factorial(n));
return 0;
}
```

## Frequently Asked Questions

**What is factorial program in C?**

The factorial of a non-negative integer is calculated via a factorial programme written in C. All positive integers up to the specified number are added together to form it. For instance, 120 is the factorial of 5 (5!).

**How to write factorial formula in C?**

Apply a loop or recursion to create a factorial formula in C. An example of a recursive method is factorial(n) = (n == 0) ? 1 : n * factorial(n - 1). For instance, 120 is the factorial of 5 (5!).

**What is the factorial of 100 factorial?**

The sum of all positive integers less than or equal to 100 factorial is known as the factorial of 100 factorial. This number is roughly equal to 9.3326215443944e+157, although it cannot be printed out in full due to its size.

## Conclusion

Understanding how to calculate factorials using recursion in C is a valuable skill that highlights the elegance and efficiency of recursive functions. By mastering this technique, you enhance your problem-solving toolkit, making it easier to tackle more complex programming challenges. Keep practicing, and you'll see just how powerful recursion can be.

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