In this work we have used Enskog theory to evaluate transport properties ind-dimensional hard spheres. In order to carry out this study we have made use of the relation between the compressibility factorZand the ratioXE/X0, whereXEis the Enskog value for a transport property andX0is that corresponding to a dilute gas. From the available numerical data forZin simulation experiences, we have calculated the aforementioned ratio for the diffusion coefficientD, the shear viscosity coefficient η, the bulk viscosity coefficient η and the thermal conductivity coefficient λ. This calculation has been extended to hard disks (d= 2), hard spheres (d= 3) and hard hyperspheres (d= 4,5) in the maximum allowable range of densities. We have also tested the suitability of some algebraic equations of state proposed for such bodies by comparing their respective values forXE/X0. Finally, we have obtained numerical values for the ratioD/DEin the casesd= 4,5. The behavior is similar to that of hard spheres.