Greatest Common Divisor
In this lab, you will implement the calculatedGCD
method in Java to find the Greatest Common Divisor (GCD) of two integers using Euclid's algorithm. The GCD of two integers is the largest positive integer that divides each of the integers without leaving a remainder.
Understanding Euclid's Algorithm
Euclid's algorithm is a timetested method to calculate the GCD of two numbers, a
and b
. The algorithm can be summarized as follows:
 If
b
is 0, then the GCD isa
.  Otherwise, calculate the GCD of
b
and the remainder ofa
divided byb
.
This process is repeated until b
becomes 0.
Implementing calculatedGCD
Your task is to implement the calculatedGCD
method in the Main
class. This method should take two integer parameters and return their GCD calculated using Euclid's algorithm.
public static int calculatedGCD(int a, int b) { // Your implementation goes here }
Edge Cases

GCD with Zero: One important edge case to consider is when one of the numbers is zero. According to the algorithm, the GCD of 0 and any number
n
isn
itself. 
GCD with One: Another edge case is when the GCD is 1. This occurs when the two numbers are coprime, meaning they have no common divisors other than 1.
Challenges
You will be tested on the following scenarios:
 Finding the GCD of 54 and 24.
 Computing the GCD of 35 and 49.
 Determining the GCD of 1 and 15 (testing coprime condition).
 Calculating the GCD of 0 and 15 (handling zero input).
Challenges Information
Challenge 1: Basic GCD Computation
 Objective: Implement the
calculatedGCD
method to correctly return the GCD of 54 and 24.  Expected Behavior: The method should return
6
as the GCD of 54 and 24, demonstrating the basic functionality of Euclid's algorithm.
Challenge 2: GCD with Prime Factors
 Objective: Write the
calculatedGCD
method to find the GCD of 35 and 49.  Expected Behavior: The method should return
7
as the GCD. This challenge tests the algorithm's ability to handle numbers with a common prime factor.
Challenge 3: Coprime Numbers GCD
 Objective: Code the
calculatedGCD
method to compute the GCD of 1 and 15.  Expected Behavior: The method should return
1
, indicating that 1 and 15 are coprime (their GCD is 1).
Challenge 4: Handling Zero as an Input
 Objective: Implement the
calculatedGCD
method that computes the GCD of 0 and 15.  Expected Behavior: The method should return
15
. This challenge checks the algorithm's handling of zero as one of the inputs, where the GCD should be the nonzero number.