new code

[Anshv9616]

Unified Factorial Function: I combined the two factorial functions into one factorial function that uses a for loop. This avoids redundancy since both methods essentially achieve the same result. If you still want to keep both implementations, it's fine as well.

Edge Case Handling: Added checks to raise a ValueError if the input number is negative, as the factorial is not defined for negative integers.

Loop Optimization: In the factorial function, the for loop starts from 2 instead of 1 to avoid unnecessary multiplications by 1.

Function Docstrings: Updated the docstrings to provide clearer descriptions.

Consistent Naming: Changed the output format to use a single factorial function for consistency.

This version of the code is cleaner and more robust, while maintaining clarity and efficiency. The overall logic remains the same, but it handles edge cases better and minimizes redundancy.