The volume of a gas increases by a factor of 2 while the pressure decreases by a factor of 3. Given that the number of moles is unaffected, the factor by which the temperature changes is:

The volume of a gas increases by a factor of 2 while the pressure decreases by a factor of 3. Given that the number of moles is unaffected, the factor by the temperature changes is: $\frac{2}{3}$ because $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$