find-gcd()

Step 1: Understand what is GCD

The Greatest Common Divisor(GCD) of two integers is the largest positive integer that divides both the numbers without leaving a remainder. This concept is used frequently in mathematical computations and also in various programming code logic. In Java, we will create a function findGCD that takes two integer parameters and returns their GCD.

Step 2: Create the Basic Structure

To start with, we create a new function findGCD. This function accepts two parameters, namely num1 and num2. These are the two numbers for which we are supposed to find the GCD.

public static int findGCD(int num1, int num2) {
  // code logic will go in here   
}

Step 3: Implement GCD Logic Using Euclid's Algorithm

Euclid's Algorithm is a popular method to calculate the GCD of two numbers. The main idea of this algorithm is that the GCD of two numbers remains the same when the larger number is replaced by its difference with the smaller number. Continue this process until both numbers become equal, which would be our GCD.

public static int findGCD(int num1, int num2) {  
    if(num1 == 0)   
       return num2;  
    return findGCD(num2%num1, num1);
}

Step 4: Handle Edge Cases

There might be cases where the user inputs a negative number. However, GCD can only be a positive number. To handle this, we take the absolute value of inputs before processing them in our findGCD function.

public static int findGCD(int num1, int num2) {
    num1 = Math.abs(num1); 
    num2 = Math.abs(num2); 
    if(num1 == 0)   
       return num2;  
    return findGCD(num2%num1, num1);  
}

Step 5: Test the findGCD function

After you have implemented the function, it is important to test it with different set of inputs to ensure it's working as expected. Here is the completed function with some test cases.

public class Main {
    public static void main(String[] args) {
        System.out.println(findGCD(60, 48)); // should return 12
        System.out.println(findGCD(-60, 48)); // should return 12
        System.out.println(findGCD(101, 103)); // should return 1
    }
    public static int findGCD(int num1, int num2) {
        num1 = Math.abs(num1); 
        num2 = Math.abs(num2); 
        if(num1 == 0)   
           return num2;  
        return findGCD(num2%num1, num1);  
    }
}