The compressibility factor for a real gas at high pressure is :

van der Waals' equation for one mole of a real gas is
$\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$
or $\mathrm{PV}=\mathrm{RT}+\mathrm{Pb}+\frac{\mathrm{ab}}{{\mathrm{V}}^2}-\frac{\mathrm{a}}{\mathrm{V}}$
At high pressures, the vander Waals' gas equation reduces to PV = RT + Pb
or     $\frac{\mathrm{PV}}{\mathrm{RT}}=1+\frac{\mathrm{Pb}}{\mathrm{RT}}$
$\therefore$Compressibility factor $\mathrm{Z}=\frac{\mathrm{PV}}{\mathrm{RT}}=1+\frac{\mathrm{Pb}}{\mathrm{RT}}$