Write a Recursive Factorial Function in Python

Define a recursive factorial function that handles edge cases and returns the product of all positive integers up to n.

Easy Python 3.9+ Aug 9, 2026 Functions & basics 14 views 0 copies

recursion factorial functions

Python code

10 lines

Python 3.9+

def factorial(n):
    """Return the factorial of n using recursion."""
    if n < 0:
        raise ValueError("Factorial is not defined for negative numbers")
    if n == 0 or n == 1:
        return 1
    return n * factorial(n - 1)

if __name__ == "__main__":
    print(factorial(5))

Output

stdout

How it works

The function checks for negative input and raises a ValueError to prevent invalid recursion. The base case returns 1 when n is 0 or 1, stopping the recursion. Each recursive call multiplies n by the factorial of n-1, breaking the problem into smaller subproblems. This works because every recursive call reduces n, so the base case is eventually reached. In the main block, factorial(5) returns 54321 = 120 and prints it.

Common mistakes

Forgetting the base case, which causes infinite recursion and a RecursionError
Not handling negative numbers, leading to infinite recursion with negative n
Using an iterative loop instead of recursion, defeating the purpose
Placing the base case after the recursive call, so it never executes

Variations

Use functools.lru_cache to memoize results for repeated calls
Write an iterative version using a loop for efficiency on large n

Real-world use cases

Calculating permutations and combinations in probability and combinatorics scripts.
Implementing recursive algorithms like generating permutations or combinations where factorial is a core step.
Estimating factorials in statistical formulas such as probability mass functions for small n.

Write a Recursive Factorial Function in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

More from Functions & basics

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