Factorial in Python: for Loop, Recursion and math.factorial()

The factorial of a nonnegative integer n, written n!, is the product of all positive integers from 1 through n. Thus 5! = 120 and 0! = 1.

Interactive Companion Jupyter Notebook

Run the Python examples, compare expected outputs, modify the code, and complete guided exercises.

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First working example

n = 6
result = 1
for i in range(1, n + 1):
    result *= i
print("Factorial:", result)

Output:

Factorial: 720

The loop starts with 1 so the same code correctly handles 0!.

Original input-based factorial loop

The original page asks the user to enter the number. Reject negative integers before calculating.

n = int(input("Enter a number: "))
if n < 0:
    print("Factorial is undefined for negative integers")
else:
    total = 1
    for i in range(1, n + 1):
        total *= i
    print("Factorial:", total)

Output:

Factorial: 720

Recursive factorial function

The original recursive code stops only at 1, which does not handle 0. This version has a base case for 0 and 1.

def fact(n):
    if n < 0:
        raise ValueError("n must be nonnegative")
    if n <= 1:
        return 1
    return n * fact(n - 1)

print(fact(4))
print(fact(0))

Output:

24
1

Use math.factorial()

Python has a standard-library function for factorials of nonnegative integers.

from math import factorial
for value in (0, 1, 5, 10):
    print(value, factorial(value))

Output:

Compare loop and recursion

Both compute identical values for small inputs; the loop avoids recursion depth limits.

from math import factorial
def factorial_loop(n):
    result = 1
    for i in range(2, n + 1):
        result *= i
    return result
for n in range(7):
    print(n, factorial_loop(n) == factorial(n))

Output:

0 True
1 True
2 True
3 True
4 True
5 True
6 True

Factorial sequence

Factorials grow quickly: 1, 1, 2, 6, 24 and 120 for 0! to 5!.

from math import factorial
print([factorial(n) for n in range(6)])

Output:

[1, 1, 2, 6, 24, 120]

Validate an invalid value

Negative integers must raise or produce a clear message, not silently return 1.

from math import factorial
try:
    print(factorial(-3))
except ValueError:
    print("Use a nonnegative integer")

Output:

Use a nonnegative integer

Common mistakes and troubleshooting

Run each example in Python 3.9 or newer. Indentation is significant in loops and functions.
Remember that input() returns a string. Convert and validate the value before doing arithmetic.
Check boundary values such as zero, negative numbers, small inputs and empty ranges.
When comparing outputs, note whether a code sample uses fixed values or user input.

Practice exercises

Try computing factorials for 0, 1, 6 and 10. Explain why a recursive base case is essential. Use the companion practice notebook for runnable examples and self-checks.

Frequently asked questions

What is 0 factorial?

0! is defined as 1.

Can factorial accept negative numbers?

No. math.factorial() raises ValueError for negative integers.

Should I use recursion for very large n?

Use an iterative algorithm or math.factorial(); recursion has depth limits.

Other related resources

Subhendu Mohapatra

Author & Instructor at plus2net

I write and maintain practical tutorials on Python, PHP, SQL, JavaScript, HTML, jQuery, and web development at plus2net. The tutorials focus on clear explanations, working examples, and code that readers can test and adapt while learning.

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