Calculating the factorial of a number in Python can be done using a simple loop or recursion. Below are two methods: iterative and recursive. For larger numbers, the iterative approach is generally more efficient and avoids recursion depth issues.

1. Iterative Approach:
   • This method uses a loop to multiply the numbers from 1 to the given number.
2. Code Example (Iterative):
   
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   def factorial_iterative(n):
       if n < 0:
           return "Factorial not defined for negative numbers"
       result = 1
       for i in range(1, n + 1):
           result *= i
       return result
   
   print(factorial_iterative(5))  # Output: 120
   

3. Recursive Approach:
   • This method calls the function itself with a smaller value until it reaches the base case.
4. Code Example (Recursive):
   
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   def factorial_recursive(n):
       if n < 0:
           return "Factorial not defined for negative numbers"
       if n == 0 or n == 1:
           return 1
       return n * factorial_recursive(n - 1)
   
   print(factorial_recursive(5))  # Output: 120
   

5. Handling Large Numbers:
   • Python can handle very large integers, so the iterative approach is better for larger values of n to avoid hitting the recursion limit.

Explanation:

• Factorial Definition: The factorial of a number n (denoted as n!) is the product of all positive integers from 1 to n. The base case is 0! = 1.
• Efficiency: The iterative approach is more efficient for larger values of n because it avoids the overhead of recursive function calls.

Both methods are valid, but the iterative approach is generally recommended for practical applications, especially with larger numbers.