C++, Класс "Rational", не могу добавить сокращение для дроби

[Александр222]

Задача
Рациональная (несократимая) дробь представляется парой целых чисел (а, 6), где а — числитель, Ь — знаменатель. Создать класс Rational для работы с ра-циональными дробями. Обязательно должна быть реализованы операции:
• сложения add, (a, b) + (с, d) = (ad + be, bd)
• вычитания sub, (a, b) - (с, d) = (ad - be, bd)
• умножения mul, (a, b) x (c, d) = (ac, bd)
• деления div, (a>b) / (c, d) = (ad, be);
• сравнения equal, greate, less.
Должна быть реализована приватная функция сокращения дроби reduce

Вопрос: Как можно реализовать приватную функцию сокращения дроби reduce? Код прилагаю, наработки по этому вопросу выделил в комментарии

Rational.h

#ifndef RATIONAL_H
#define RATIONAL_H

#include <iostream>
#include <sstream>

class Rational {

private:
    int Numerator{};
    int Denominator{};
    
    /*int GetReduced() {

        int nod(int a, int b);
        int mod = 1;

        if (Numerator == 0 && Denominator == 0) return 0;

        Numerator = abs(Numerator);
        Denominator = abs(Denominator);

        if (Numerator == Denominator) return Numerator;

        if (Denominator > Numerator) {
            mod = Numerator;
            Numerator = Denominator;
            Denominator = mod;
        }
        if (Denominator == 0) return Numerator;

        while (mod) {
            mod = Numerator % Denominator;
            if (mod) {
                Numerator = Denominator;
                Denominator = mod;
            }
        }
        return Denominator;
    }*/

public:
    Rational() = default;
    Rational(int Numerator, int Denominator);
    Rational(const Rational& R);

    void SetNumerator();
    void SetDenominator();

    int GetNumerator() const;
    int GetDenominator() const;
    
    friend Rational operator + (const Rational& a, const Rational& b);
    friend Rational operator - (const Rational& a, const Rational& b);
    friend Rational operator * (const Rational& a, const Rational& b);
    friend Rational operator / (const Rational& a, const Rational& b);
    friend bool operator > (const Rational& a, const Rational& b);
    friend bool operator < (const Rational& a, const Rational& b);
    friend bool operator == (const Rational& a, const Rational& b);
    friend bool operator != (const Rational& a, const Rational& b);

    friend std::ostream& operator << (std::ostream& out, const Rational&);
    friend std::istream& operator >> (std::istream& in, Rational&);
};


#endif

Rational.cpp

#include <iostream>
#include "Rational.h"

Rational::Rational(int Numerator, int Denominator): Numerator(Numerator), Denominator(Denominator) {}
Rational::Rational(const Rational& R): Numerator{ R.Numerator }, Denominator{ R.Denominator } {}

void Rational::SetNumerator(){}
void Rational::SetDenominator(){}

int Rational::GetNumerator() const { return Numerator; }
int Rational::GetDenominator() const { return Denominator; }


/*Rational GetReduced(){
    int gcd = GetGCD(GetNumerator(), GetDenominator());
    int Numerator = GetNumerator() / gcd;
    int Denominator = GetDenominator() / gcd;
    if (Denominator < 0) {
        Numerator = -Numerator;
        Denominator = -Denominator;
    }
    return Rational(Numerator, Denominator);
}*/


double GetGCD(int& a, int& b) {
    int x = std::abs(a);
    int y = std::abs(b);
    while (1) {
        x = x % y;
        if (x == 0) {
            return y;
        }
        y = y % x;
        if (y == 0) {
            return x;
        }
    }
}

Rational operator + (const Rational& a, const Rational& b) {
    return Rational(a.GetNumerator() * b.GetDenominator() + b.GetNumerator() * a.GetDenominator(), a.GetDenominator() * b.GetDenominator());
}

Rational operator - (const Rational& a, const Rational& b) {
    return Rational(a.GetNumerator() * b.GetDenominator() - b.GetNumerator() * a.GetDenominator(), a.GetDenominator() * b.GetDenominator());
}

Rational operator * (const Rational& a, const Rational& b) {
    return Rational(a.GetNumerator() * b.GetNumerator(), a.GetDenominator() * b.GetDenominator());
}

Rational operator / (const Rational& a, const Rational& b) {
    return Rational(a.GetNumerator() * b.GetDenominator(), a.GetDenominator() * b.GetNumerator());
}

/*std::ostream& operator << (std::ostream& out, const Rational& R) {
    Rational reduced = R.GetReduced();
    return out << reduced.GetNumerator() << "/" << reduced.GetDenominator();
}*/

bool operator > (const Rational& a, const Rational& b) { return (a.GetNumerator()/b.GetNumerator()) > (a.GetDenominator()/b.GetDenominator()); }

bool operator < (const Rational& a, const Rational& b) { return (a.GetNumerator() / b.GetNumerator()) < (a.GetDenominator() / b.GetDenominator()); }

bool operator == (const Rational& a, const Rational& b) { return (a.GetNumerator() == b.GetNumerator() && a.GetDenominator() == b.GetDenominator()); }

bool operator != (const Rational& a, const Rational& b) { return !(a == b); }

std::ostream& operator << (std::ostream& out, const Rational& R) { 
    out << "Numerator, Denominator: " << R.Numerator << ", " << R.Denominator;
    return out;
};

std::istream& operator >> (std::istream& in, Rational& R) {
    in >> R.Numerator >> R.Denominator;
    return in;
};