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

Van der Waals equation for 1 mole: $(P+\frac{a}{V^2})(V-b)=RT$.At high pressure, the volume $V$ is small, so the term $\frac{a}{V^2}$ is much smaller compared to $P$ (or rather, $P$ is very large, so we ignore $a$).Equation simplifies to $P(V-b)=RT⟹PV-Pb=RT$.Dividing by $RT$:$\frac{PV}{RT}-\frac{Pb}{RT}=1$$Z=1+\frac{Pb}{RT}$.