Lab 15.1 Greatest Common DivisorA formula for finding the greatest common divisor (GCD) of two numbers was formulated by themathematician Euclid around 300 BCE. The GCD of two numbers is the largest number that will divideinto both numbers without any remainder. For example, the GCD of 12 and 16 is 4, the GCD of 18 and12 is 6.The basic algorithm is as follows:Assume we are computing the GCD of two integers x and y. Follow the steps below:1. Replace the larger of x and y with the remainder after (integer) dividing the larger number by thesmaller one.2. If x or y is zero, stop. The answer is the nonzero value.3 If neither x nor y is zero, go back to step 1.Here is an example listing the successive values of x and y:$ (135 / 20) - 15$ (20 / 15) = 5* (15 / 5) = 01352015201555GCD = 5Write a recursive method that finds the GCD of two numbers using Euclid's algorithm.public class Arithmetic{public static int gcd(int a, int b)// Your work hereLab 15.2 Tester for GCDWrite a tester program for your GCD algorithm.

Program code: import java.util.*;import java.lang.*;public class Main{ //Method to find gcd of 2…

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Lab 15.2 Tester for GCD Write a tester program for your GCD algorithm.

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Question

Lab 15.1 Greatest Common Divisor
A formula for finding the greatest common divisor (GCD) of two numbers was formulated by the
mathematician Euclid around 300 BCE. The GCD of two numbers is the largest number that will divide
into both numbers without any remainder. For example, the GCD of 12 and 16 is 4, the GCD of 18 and
12 is 6.
The basic algorithm is as follows:
Assume we are computing the GCD of two integers x and y. Follow the steps below:
1. Replace the larger of x and y with the remainder after (integer) dividing the larger number by the
smaller one.
2. If x or y is zero, stop. The answer is the nonzero value.
3 If neither x nor y is zero, go back to step 1.
Here is an example listing the successive values of x and y:
$ (135 / 20) - 15
$ (20 / 15) = 5
* (15 / 5) = 0
135
20
15
20
15
5
5
GCD = 5
Write a recursive method that finds the GCD of two numbers using Euclid's algorithm.
public class Arithmetic
{
public static int gcd(int a, int b)
// Your work here
Lab 15.2 Tester for GCD
Write a tester program for your GCD algorithm.

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