Factorial Calculator in Python

What is factorial?

The factorial of a number is the multiplication of all the numbers between 1 and the number itself. It is a mathematical operation written like this: n!. It's a positive integer. Factorial is not defined for negative numbers.

For example, the factorial of 3 is 3! (= 1 × 2 x 3).

In this Python tutorial, we'll learn the various methods to calculate the factorial of a number in Python.

How to calculate the factorial of a number in Python?

1. Using While Loop/Iterative approach

def factorial(n):
    if n < 0:
           print("Sorry, factorial is undefined for negative numbers")
    elif n == 0 or n == 1:
        return 1
    else:
        fact = 1
        while(n > 1):
            fact *= n
            n -= 1
        return fact

num = 8
print("Factorial of",num,"is",
factorial(num))   

In the above code, we check if the number is negative, zero, or positive using the if...elif...else statement. If the number is positive, we use the while loop in python to calculate the factorial.

Output

Factorial of 8 is 40320

2. Using Recursion

def factorial(n):
    
    # single line to find factorial
    return 1 if (n==1 or n==0) else n * factorial(n - 1) 

# Driver Code
num = 5
print("Factorial of",num,"is",factorial(num))

In the above code, factorial() is a recursive function that calls itself. Here, the function will recursively call itself by decreasing the value of the num.

Output

Factorial of 8 is 40320

3. Using One line Solution (Using Ternary operator)

def factorial(n):

    # single line to find factorial
    return 1 if (n==1 or n==0) else n * factorial(n - 1) 

num = 8
print ("Factorial of",num,"is",
      factorial(num))

Output

Factorial of 8 is 40320

4. Using Built-In Function

import math

def factorial(n):
    return(math.factorial(n))

num = 8
print("Factorial of", num, "is",
      factorial(num))

In the above code, we've used the math module that contains the math.factorial() function to calculate the factorial of any given number.

Output

Factorial of 8 is 40320

5. Using numpy.prod

import numpy
num=8
fact=numpy.prod([i for i in range(1,num+1)])
print("Factorial of", num, "is",
      fact)

In the above code, we've used the numpy module that contains the numpy.prod() function to calculate the factorial of any given number.

Output

Factorial of 8 is 40320

6. Using the Prime Factorization Method

def primeFactors(n):
    factors = {}
    i = 2
    while i*i <= n:
        while n % i == 0:
            if i not in factors:
                factors[i] = 0
            factors[i] += 1
            n //= i
        i += 1
    if n > 1:
        if n not in factors:
            factors[n] = 0
        factors[n] += 1
    return factors

# Function to find factorial of a number
def factorial(n):
    result = 1
    for i in range(2, n+1):
        factors = primeFactors(i)
        for p in factors:
            result *= p ** factors[p]
    return result

num = 8
print("Factorial of", num, "is", factorial(num))

In the above code,

1. First, initialize the factorial variable to 1.
2. For each number i from 2 to n:
   1. Find the prime factorization of i.
   2. For each prime factor p and its corresponding power k in the factorization of i, multiply the factorial variable by p raised to the power of k.
3. Return the factorial variable.

Output

Factorial of 8 is 40320

Summary

In the above tutorial, we learned various methods to calculate the factorial of a number in Python. Before trying these methods, you must be clear with the fundamental concepts of loops, recursion, modules, functions, etc. Just refer to these tutorials and come back to learn factorial calculation in Python.