text: #=============================================================================#
  #
  #    File:   euclidean_algorithm.py
  #    Author: Jack Morgan
  #    Date:   May 2021
  #    Description:
  #        Recursive function for the euclidean algorithm
  #        Computes the greatest common divisor (highest common factor) of two numbers a and b
  #
  #=============================================================================#
  
  
  # function to find the greatest common divisor of two integers
  def gcd(num1: int, num2: int) -> int:
      if num2 == 0:
          return num1
      else:
          print('--------------')
          print('a = b * n + r')
          print(f'{num1} = {num2} * n + r')
          print(f'{num1} = {num2} * {num1 // num2} + {num1 % num2}')
          print('--------------')
          return gcd(num2, num1 % num2)
  
  