How To Find Factorial in Python [With Coding Examples]

Introduction

Everyone one of us must be familiar with the word factorial as we all got introduced to that in our primary school in Mathematics subject. Factorial is the product of all positive integers starting from one to the given number. Factorial is only calculated for positive values and cannot be calculated for Negative and Float types.

I wondered when I am learning factorial and other mathematical concepts that where I would be using them in my real life, thanks to Data Science as I was able to understand now the importance of all the mathematical components such as Linear Algebra, Probability, Statistics.

Let us see the importance of the Factorial, different ways to calculate it using python in this article.

Importance

Let us take an example that we have a race between 10 cars in a world race event, and we have a problem statement to find out how many ways that those 10 cars come first, second, third. As there are only 10 cars, we would like to just take a paper and write down the various combinations. But what if we have 100 cars or more events and we have the same or similar kind of problem statement in that?

In order to tackle these kinds of situations, we have something called Permutation. I guess you would be aware of this term as Permutations and Combinations in our primary school. These are very much needed if you want to ace your Data Analysis and statistical skills. If you are a beginner and interested to learn more about data science, check out our data science courses from top universities. This helps to solve the problem statement as stated below.

Solution

We have a total of 10 cars.

We need to find the possibility of 3 winners out of 10.

10! / (10-3)! = 10! / 7! = 720

So, we have a total of 720 possibilities for these 10 cars to come first, second, third in the race event. 

Python Implementation

Python is a high-level, interpreted and general-purpose programming language that focuses on code readability and the syntax used in Python Language helps the programmers to complete coding in fewer steps as compared to Java or C++ and it is built on top of C.

The language was founded in 1991 by the developer Guido Van Rossum. Python is widely used in bigger organizations because mainly in various Artificial Intelligence use cases such as Computer Vision, Natural Language Processing , Deep Learning , Speech Recognition, Face Recognition, Voice Recognition.

Python is a very powerful programming tool and can be used for a wide variety of use cases in real life. It offers a direct function that can compute the factorial of a given number without writing the code explicitly. But let us start with a naïve approach and at last get to know about that function.

Also Read: Why Python so popular with developers?

For Loop

We can calculate the factorial of a number by iterating from number 1 till the given number by multiplying at each step. Let us jump into the coding part of the above discussed approach.

Code

number = input (“Enter a Number:”) # Ideally you can use any print message

factorial = 1

if int (number) >=1: # To check whether the given number is positive or not.

for i in range (1, int(number)+1): # Loop from number 1

   factorial = factorial * I   # Multiplication with each number.

print (“Factorial of “, number, ” is: “, factorial) # Print out the calculated factorial.

Output

Running the above code will give you the below output:

Enter a Number :5

Factorial of 5 is: 120

Recursive Function

In this case we will be creating our own user defined function in python that will help us to calculate the factorial of a given number.

Code

number = input (“Enter a number: “)

def recursive_factorial(number): # User defined recursive function.

if number == 1: # Condition if the given number is equal to 1

   return number

elif number < 1: # Condition if given number is lesser than 1

   return (“The given number is lesser than one and the factorial cannot be calculated.”)

else:

   return number*recursive_factorial(number – 1)

print (recursive_factorial(int(number)))

Output

Running the above code will give you the below output:

Enter a number: 5

120

Enter a number: -2

The given number is lesser than one and the factorial cannot be calculated

Enter a number: 1

1 

Factorial function in Math Package

Python is extensively known for its ease of use and user-friendly third party packages which will simplify many tasks. In the current scenario Python is the go-to language for Data Scientists.

Code

import math # Required package

number= input(“Enter a number: “)

print(“The factorial of “, number, ” is : “)

print(math.factorial(int(number))) # Function to calculate the factorial

Output

Running the above code will give you the below output:

Enter a number: 5

The factorial of 5 is :

120

Enter a number: 5.6

Traceback (most recent call last):

The factorial of 5.6 is :

File “C:/Users….py”, line 5, in

print(math.factorial(int(number)))

ValueError: invalid literal for int() with base 10: ‘5.6’

 We are getting a value error because we cannot calculate the Factorial of float integer. When we are explicitly writing the python code we need to take care to check all the condition and output the relevant message, but in the factorial function of Math package in python it does everything for us which helps us to decrease our lines code when we have usage of Factorial in our Project or any problem statement.

Must Read: Python Tutorial

Conclusion

In this article we got to know the importance and application of Factorial and other important mathematical concepts in real life. Went through the different types of code to calculate the Factorial of a given number. This article just covers the Factorial in Python but there are many other mathematical calculations available in the MATH package. Folks new to Python can have a deeper look into them and can even try a few.

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What is recursion in Python?

Recursion in Python means looping through the data to reach a definite result. It is a well-known mathematical and programming process in which something (a statement or a function) is defined in terms of itself. With the help of recursion, Users or developers can split complex codes and functions into smaller subparts, and creating a sequence becomes much more accessible. A developer should take extra care when using recursion since writing a function that never terminates or consumes excessive amounts of memory or CPU power is quite frequent. When done correctly, recursion may be a tremendously efficient and mathematically innovative way to program.

How much time does it take to learn Python basics?

Python is considered the simplest programming language, so learning the basics of Python is easy and is not very time-consuming. Students or professionals can devote 1-2 months to learn the basics of Python. A professional can also master all of the essential python functions and libraries within 4-5 months by dedicating around 2-3 hours every day. Grasping Python is easy since most of the codes have lesser statements, and there are more predefined functions.

What is the time complexity of the factorial program in Python?

We discovered from the factorial program that factorial(0) is simply one comparison (1 unit of time) and factorial(n) is one comparison, one multiplication, one subtraction, and time for factorial (n-1). So we can say that T(n) = T(n — 1) + 3 and T(0) = 1. Putting values, we find that T(N) is directly proportional to n, as seen in Big-Oh notation. As a result, the temporal complexity of the factorial program is O(n).

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