write a python function to calculate factorial using recursion. include the code in a properly formatted code block with syntax highlighting

Certainly! Here’s a Python function to calculate the factorial of a number using recursion:

```python
def factorial(n):
    """Calculate the factorial of a number n using recursion."""
    if n < 0:
        raise ValueError("Factorial is not defined for negative numbers")
    elif n == 0 or n == 1:
        return 1
    else:
        return n * factorial(n - 1)

# Example usage:
# print(factorial(5))  # Output: 120
```

In this function, we check if the input is a negative number, in which case we raise a `ValueError`. If the input is 0 or 1, we return 1, as the factorial of both these values is 1. For any other positive integer, we call the `factorial` function recursively.

Update (2026-06-17):
Here is a Python function that calculates the factorial of a number using recursion:

```python
def factorial(n):
    if n < 0:
        raise ValueError("Factorial is not defined for negative numbers.")
    elif n == 0 or n == 1:
        return 1
    else:
        return n * factorial(n - 1)

# Example usage
print(factorial(5))  # Output: 120
```

This function checks if the input is negative and raises an exception if so. For the base cases of 0 and 1, it returns 1. Otherwise, it computes the factorial recursively.