By means of the effective-field theory (EFT) with correlations, the thermodynamic and magnetic quantities such as magnetization, susceptibility, internal energy, free energy, hysteresis curves and compensation behaviors of the spin-1/2 hexagonal Ising nanowire (HIN) system with core/shell structure have been presented. The hysteresis curves are obtained for different values of the system parameters on both ferromagnetic and antiferromagnetic case. It has been shown that the system only undergoes a second-order phase transition. Moreover, from the thermal variations of the total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types.