Let d = gcd (x, y). Then x = dx_{1} and y = dy_{1}. We observe that 2x + 7y divides 7x + 2y if and only if 2x_{1} + 7y_{1} divides 7x_{1} + 2y_{1}. This means 2x_{1} + 7y_{1} should divide 49x_{1} + 14y_{ 1}. But 2x_{1} + 7y_{1} divides 4x_{1} + 14y_{1}. Hence 2x_{1} + 7y_{1} divides 45x_{1}. Similarly, we can show that 2x_{1} + 7y_{1} divides 45x_{1}. Hence 2x_{1} + 7y_{1} divides gcd(45x_{1}, 45y_{1}) = 45gcd(x_{1}, y_{1}) = 45. Hence