Factorial Program in Python

What is a factorial

The factorial of a number n (written n!) is the product of all whole numbers from 1 up to n. For example, 5! = 1 × 2 × 3 × 4 × 5 = 120. We can compute it in Python with a loop, with recursion, or with a built-in function.

Factorial with a loop

n = 5
f = 1
for i in range(1, n + 1):
    f = f * i
print("Factorial:", f)

We start f at 1 and multiply it by each number from 1 to n. range(1, n+1) goes 1, 2, 3, 4, 5 — note the +1 so n is included.

Dry run of the loop

Factorial with recursion

Recursion means a function that calls itself with a smaller value.

def factorial(n):
    if n == 0:          # base case
        return 1
    return n * factorial(n - 1)

print(factorial(5))

factorial(5) becomes 5 × factorial(4), then 4 × factorial(3), down to factorial(0) which returns 1. Then the results multiply back up to 120.

Using math.factorial

For real code, Python already has a factorial function.

import math
print(math.factorial(5))

math.factorial is the fastest and safest choice. You write your own loop or recursion mainly to understand how it works.

Common mistakes

• Wrong range. Use range(1, n+1); without +1 you miss n itself.
• Starting f at 0. Start at 1 — multiplying by 0 gives 0 forever.
• Missing the base case in recursion. Without if n == 0: return 1, recursion never stops.
• Recursion on huge numbers. Very large n can hit Python's recursion limit — use a loop or math.factorial.

Summary

• Factorial n! is the product of all whole numbers from 1 to n.
• With a loop: start f at 1 and multiply by each i in range(1, n+1).
• With recursion: n * factorial(n-1), base case 0! = 1.
• For real code, use math.factorial(n).
• Remember 0! = 1 and that factorials grow very fast.

Next, try the prime number program, or revise Python loops.