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A factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. Mathematically: n! = n × (n-1) × (n-2) × ... × 1 and by definition 0! = 1.
Recursion is a natural way to compute factorials, where a function calls itself with a smaller argument until it reaches a base case.
Example Implementation:
def factorial_recursive(n):# Handle invalid inputif n < 0:return "Factorial not defined for negative numbers"# Base caseif n == 0 or n == 1:return 1# Recursive casereturn n * factorial_recursive(n - 1)# Example usagenum = 5print(f"{num}! = {factorial_recursive(num)}")Copied!✕CopyOutput:
5! = 120Copied!✕CopyHow it works:
Base Case: Stops recursion when n is 0 or 1, returning 1.
Recursive Step: Multiplies n by the factorial of n-1.
Termination: Each call reduces n until it reaches the base case.
Trace for factorial_recursive(4):
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