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How to Implement the Euclidean Algorithm in Python

Submitted by razormist on Monday, February 10, 2025 - 22:22.

In this tutorial, we’ll learn how to program "How to Implement the Euclidean Algorithm in Python." The objective is to safely and efficiently compute the greatest common divisor (GCD) of two numbers using the Euclidean Algorithm. This tutorial will guide you through the process step by step, ensuring a clear understanding of the algorithm and its implementation in Python. So, let’s get started!

This topic is straightforward to understand. Just follow the instructions I provide, and you’ll complete it with ease. The program I’ll demonstrate will show you the proper way to use the Euclidean algorithm to calculate the greatest common divisor (GCD). So, let’s dive into the coding process!

Getting Started:

First you will have to download & install the Python IDLE's, here's the link for the Integrated Development And Learning Environment for Python https://www.python.org/downloads/.

Creating Main Function

This is the main function of the application. The following code will display a simple GUI in terminal console that will display program. To do this, simply copy and paste these blocks of code into the IDLE text editor.
  1. def gcd(a, b):
  2.         if a == 0 :
  3.                 return b
  4.        
  5.         return gcd(b%a, a)
  6.  
  7.  
  8. while True:
  9.         print("\n================= Implement the Euclidean Algorithm =================\n\n")
  10.    
  11.         a = int(input("Enter the 1st number: "))
  12.         b = int(input("Enter the 2nd number: "))
  13.         print("gcd(", a , "," , b, ") = ", gcd(a, b))
  14.  
  15.         opt = input("\nDo you want to try again?(yes/no): ")
  16.  
  17.         if opt.lower() == 'yes':
  18.                 ret=False
  19.         elif opt.lower() == 'no':
  20.                 ret=True
  21.                 print("Exiting program....")
  22.         else:
  23.                 print("Please enter yes/no:")
  24.                 break
  25.  
  26.         if ret == False:
  27.                 continue

This program calculates the greatest common divisor (GCD) of two numbers using the Euclidean Algorithm. The algorithm works by recursively computing the remainder of the division until one of the numbers becomes zero, at which point the other number is the GCD. The program runs in a loop, allowing users to repeatedly enter numbers and find their GCD until they choose to exit.

Output:

There you have it we successfully created How to Implement the Euclidean Algorithm in Python. I hope that this simple tutorial help you to what you are looking for. For more updates and tutorials just kindly visit this site. Enjoy Coding!

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