# Factorial Calculator in Python

11 May 2024
Beginner
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## 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.

 iteration fact*i (returned value) 1 8*1=8 2 8*7=56 3 56*6=336 4 336*5=1680 5 1680*4=6720 6 6720*3=20160 7 20160*2=40320 8 40320*1=40320

#### 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``
 Read More: Recursion in Data Structures

### 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
``````
 Read More: What are Operators in Python?

### 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
``````
 Read More: Python Functions - A Complete Guide

### 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.

## FAQs

### Q1. How do you code a factorial in Python?

You can code a factorial in Python using recursion, iteration, ternary operator,
built-In function, numpy.prod, and prime factorization method.

### Q2. What is the logic of factorial?

Factorial logic involves multiplying a number by all positive integers less than itself, recursively reducing the problem until reaching the base case of factorial(1) = 1.

### Q3. What is the factorial formula in programming?

The factorial formula in programming is typically expressed as n!=n×(n−1)×(n−2)×…×1, where n is a non-negative integer. It represents the product of all positive integers from 1 to 𝑛, inclusive.

### Q4. What is an example of a factorial?

An example of a factorial is 5!, which equals 5×4×3×2×1-=120
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