- 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.

See the following implementation of the algorithm.

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})); } }

Here is the output for 15, 18, 42 and 108

Here is the output for 3,7 and 12