Factorial of a Number - Python

Given an integer n, the task is to compute its factorial, i.e., the product of all positive integers from 1 to n. Factorial is represented as n! and is commonly used in mathematics, permutations and combinatorics. For Example:

Input: n = 6
Output: 720
Explanation: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Let's explore different methods to find the factorial of a number in Python.

Using math.factorial()

This method computes the factorial using Python’s built-in factorial() function, which performs the entire calculation internally without requiring loops or recursion in user code.

import math
n = 6
print(math.factorial(n))

720

Using NumPy’s np.prod()

NumPy performs multiplication through optimized C-level operations. It computes the factorial by multiplying all numbers from 1 to n in a single vectorized step using np.prod().

import numpy as np
n = 6
print(np.prod(range(1, n+1)))

720

Explanation:

• range(1, n+1) generates numbers from 1 through n.
• np.prod(...) multiplies all values in the sequence.

Using an Iterative For Loop

This method calculates factorial by manually multiplying the numbers from 1 to n inside a for loop.

n = 6
f = 1

for i in range(1, n+1):
    f *= i

print(f)

720

Explanation:

• f = 1 starts with an initial multiplication value.
• f *= i multiplies f with each number i from 1 to n.
• Produces the factorial after the loop completes.

Using a Recursive Function

This approach follows the mathematical definition of factorial by repeatedly calling the function with decreasing values until reaching the base case.

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

print(fact(6))

720

Explanation:

• n <= 1 base condition returning 1.
• n * fact(n-1) multiplies the current number with the factorial of the previous number.