Calculate the Factorial of a Positive Integer

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1. The Challenge: Calculating Factorials

Create a function factorial(num) that takes an integer and returns its factorial (num!). For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

2. Why It Matters

Factorials are fundamental in combinatorics, probability, permutations, and algorithm analysis.

3. The Python Solution

You can solve factorials using recursion, a loop, or the built-in math.factorial() module:

# Recursive Approach
def factorial(num):
    if num <= 1:
        return 1
    return num * factorial(num - 1)

# Testing our function
print(factorial(3)) # Output: 6
print(factorial(5)) # Output: 120
print(factorial(1)) # Output: 1
print(factorial(0)) # Output: 1

4. Built-in Math Module

Python includes a built-in math.factorial():

import math
print(math.factorial(5)) # Output: 120

5. Common Mistakes

• Base Case Missing in Recursion: Forgetting if num <= 1: return 1 causes infinite recursion until Python raises RecursionError: maximum recursion depth exceeded.
• Handling 0!: By mathematical definition, 0! = 1. Ensure your base case returns 1 for zero.

6. Next Steps

Include base cases in recursive functions. Next, let's check if a list includes a specific element!