Is there a better version for verbosing the output of the euclidean method?

Here is my implementation of the Euclidean Algorithm. My question is how to make it more "professional". It's working right, but isn't this too newbie?

public class Euklideszi {

    public int Euklideszi(int a, int b, boolean lepesrolLepesre) {
        int r = a % b;
        if (a < b) {
            r = a;
            a = b;
            b = r;
        }
        if (a % b == 0) {
            if (lepesrolLepesre) {
                System.out.println("A legnagyobb közös osztó: " + b);
            }
            return b;
        } else {
            while (r != 0) {
                r = a % b;
                if (lepesrolLepesre) {
                    System.out.println(a + "=" + a / b + "*" + b + "+" + r);
                }
                a = b;
                b = r;
            }
            if (lepesrolLepesre) {
                System.out.println("A legnagyobb közös osztó: " + a);
            }
            return a;
        }

    }

 }

There are a couple of "newbie" things here, yes.

-
Your method has an uppercase first character, it should be lower-case.

-
Your method is not static, which means that an instance of the class has to be created just to use your method. You can make the method static, and add a private constructor to the class so that it can't be initialized from outside.

-
As @skiwi says in a comment, please use English identifier names when you code.

-
boolean lepesrolLepesre is used to toggle whether or not the method should log anything to console. This is a bad thing. A method like this should not output anything to the console, it should simply return the result.

-
This code:

if (a < b) {
    r = a;
    a = b;
    b = r;
}

is used to switch so that a always is the largest variable, and it's using r as a temporary variable. Even though this works, I would use a temp variable here that's only visible in this scope.

if (a < b) {
    int temp = a;
    a = b;
    b = temp;
}
int r = a % b;

Note that here, I put the initial calculation of r after this switch has taken place.

-
There is no need to use the else as you return inside the if. You can remove else and reduce the indentation there.

Edit:

In the comments below you asked for a cleaner way for the user to see every step, you can accomplish this by using a callback interface.

Then you can modify your code to:

public static interface EuklidesStepCallback {
    void onStep(int a, int b, int r);
}
public static int gcd(int a, int b, EuklidesStepCallback callback) {
    ...
    while (r != 0) {
        r = a % b;
        if (callback != null) {
            callback.onStep(a, b, r);
        }
        a = b;
        b = r;
    }
    return a;
}   

public static void main(String[] args) {
    EuklidesStepCallback callback = new EuklidesStepCallback() {
        @Override
        public void onStep(int a, int b, int r) {
            System.out.println(a + "=" + a / b + "*" + b + "+" + r);
        }
    };
    System.out.println(gcd(24, 16, callback));
}

If you're able to use Java 8, you can use a lambda for the callback:

public static void main(String[] args) {
    System.out.println(gcd(24, 16, (a, b, r) -> System.out.println(a + "=" + a / b + "*" + b + "+" + r)));
}

This callback system is more flexible in case you'd want to save each of the steps to a List or similar.

StackExchange Code Review Q#55262, answer score: 6