Teachers

• In this algorithm we first find the smallest integer in the int array. 
• Then we get the modulus for each element in the numbers of the array by dividing smallest integer and add all those modulus together. 
• After processing each element in the array we check if the total of modulus is equals to 0.  If it is equal to 0 then the GCD is  current smallest value if that total is not equals 0 we deduct 1 from the previous smallest value and do the same computation. 
• The algorithm will continue with  the same operations until total of modulus becomes 0 or until smallest integer is 2.
• If there is any GCD, algorithm will return it or otherwise it will return -1.

public class GCD {

    public static int findGcd(int... numbers) {

        //Find the smallest integer in the number list
        
        int smallest = numbers[0];

        for (int i = 1; i < numbers.length; i++) {
            if (numbers[i] < smallest) {
                smallest = numbers[i];
            }
        }

        //Find the GCD
        while (smallest > 1) {
            
            int counter = 0;
            int modTot = 0;
            
            while (counter < numbers.length) {

                modTot += numbers[counter] % smallest;
                counter++;

            }

            if (modTot == 0) {
                //Return the gcd if any
                return smallest;
            }

            //System.out.print(" "+ smallest);
            smallest--;

        }
        //return -1 if there is no gcd
        return -1;
    }

    public static void main(String[] x) {
        System.out.println("The GCD of 15 18 42 108 : "+GCD.findGcd(new int[]{15, 18, 42,108}));
    }
}