Python programs / Numbers / Factorial of a number

Python Program to Find the Factorial of a Number

Beginner Numbers

Finds the factorial of a number, the product of every whole number from 1 to n, with a for loop.

The factorial of a whole number n, written n!, is the product of every whole number from 1 to n: 5! = 1 × 2 × 3 × 4 × 5 = 120. It counts the ways to put n things in order, so 5 books can stand on a shelf in 120 different orders. By definition, 0! is 1.

Program

def factorial(n):
    """The factorial of n: 1 * 2 * 3 * ... * n."""
    result = 1
    for number in range(1, n + 1):
        result *= number
    return result


print("5! =", factorial(5))
print("0! =", factorial(0))

Open in the editor Download factorial.py

Output

5! = 120
0! = 1

How it works

  1. result starts at 1, not 0, as multiplying anything by 0 would give 0.
  2. The loop multiplies result by every number from 1 to n. range(1, n + 1) stops before n + 1, so n itself is included. result *= number is short for result = result * number.
  3. After the loop, result holds the product, and the function returns it.
  4. The program works out 5! and 0!. For 0, range(1, 1) is empty, so the loop never runs and the function returns the 1 it started with, which is the right answer.

For 5, result goes like this:

number result
1 1 × 1 = 1
2 1 × 2 = 2
3 2 × 3 = 6
4 6 × 4 = 24
5 24 × 5 = 120

Other ways to write it

With recursion

n! is n × (n − 1)!, so the function can call itself with a smaller number until it reaches 1 (recursion). Python allows about 1000 calls inside each other, so a large n, such as 5000, fails with a RecursionError, which the loop never does.

def factorial(n):
    if n <= 1:
        return 1
    return n * factorial(n - 1)

print(factorial(6))

With math.factorial()

The standard library has it built in, written in C, so it's faster. It raises a ValueError for a negative number.

import math

print(math.factorial(10))

Try it yourself

  • Work out 10! and 20!. 20! is 2432902008176640000: Python's whole numbers grow as big as they need to.
  • Print 1! to 10! with a loop, one per line.
  • For a negative n, the function returns 1, which is wrong. Make it raise a ValueError instead (errors and exceptions).
  • Count the zeros at the end of 25!: there are 6.

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