Pressure change when volume and temperature both increase

By what factor does the pressure change if:


* the temperature rises from 0 to 100 degrees Celsius,
* and the volume is doubled?


$$
\pu{0 °C} = \pu{273.2 K}\\
\pu{100 °C} = \pu{373.2 K}
$$


Assuming $pV = nRT$:


Since pressure is proportional to temperature, neglecting the change in volume, the pressure would increase by a factor of $$\frac{373.2}{273.2} = 1.366\ .$$


Now since the volume is doubled as well, can I simply conclude that the pressure increases by a factor of $$\frac{1.366}{2} = 0.683\ ?$$


This is a task from a introduction to gases, I've mainly used the ideal gas law $pV = nRT$, but I wanna make sure my logic isn't flawed from the beginning.


