НОД - 3 начина

public class First {
    static int gcd(int a, int b) {
        if (a > b) {
            return gcd(a - b, b);
        } else if (b > a) {
            return gcd(a, b - a);
        } else {
            return a;
        }
    }

    public static void main(String[] args) {
        System.out.println(gcd(15, 3));
    }
}

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public class Second {
    static int gcd(int a, int b) {
        if (a > b) {
            return gcd(a - b, b);
        } else if (b > a) {
            return gcd(a, b - a);
        } else {
            return a;
        }
    }

    public static void main(String[] args) {
        System.out.println(gcd(8, 4));
    }
}

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public class Third {
    static int gcd(int a, int b) {
        for(int i = Math.min(a, b); i >= 1; i--) {
            if(a % 1 == 0 && b % 1 == 0) {
                return i;
            }
        }
        return 1;
    }
    public static void main(String[] args) {
System.out.println(gcd(10,5));
    }

}