$1$ The Euclidean Algorithm

The $GCD$ of two integers, denoted $GCD(x,y),$ is the largest integer that divides both $x$ and $y.$ For example, the GCD of $21$ and $9,GCD(21,9),$ is $3.$ The GCD is an important concept in mathematics and makes regular appearances in the areas of number theory and abstract algebra.

The ancient mathematician Euclid formulated a relatively simple algorithm for computing the GCD of two integers $x$ and $y($assume $x>y).$ The algorithm for computing $GCD(x,y)$ proceeds as follows

Calculate the remainder of the division $\frac{x}{y}.$ Denote the value by $r.$

If $r=0$ then $GCD(x,y)=y.$ Otherwise, set $y=x$ and $x=r$ then return to the previous step.

For this example, you will implement a Euclidean Algorithm that takes two integers as inputs and computes their GCD$.$

Create a class called EuclideanAlgorithm that contains a main method.

In the EuclideanAlgorithm class, create a public method called GCD that takes two int parameters called $x$ and $y$ as inputs and returns an int.

In the GCD method, declare an int variable called remainder that stores the remainder of $\frac{x}{y}($Hint: Use the modulus operator$).$

Use a while loop to implement the repeated portion of Euclid's Algorithm.

Once the GCD has been computed, return the value. Test your code a few times in the main method. A few test cases are provided below:

$\backslash$table$[[x,y,GCD$