The ab initio full-potential linearized augmented plane-wave method explicitly designed for the slab geometry was employed to elucidate the physical origin of the layer potentials for the trilayers nFe/3Cr/nFe(001), where n is the number of Fe monolayers. The thickness of the transition-metal ferromagnet has been ranged from n = 1 up to n = 8 while the spacer thickness was fixed to 3 monolayers. The calculated potentials were inserted in the Fuchs-Sondheimer formalism in order to calculate the giant magnetoresistance (GMR) ratio. The predicted GMR ratio was compared with the experiment and the oscillatory behavior of the GMR as a function of the ferromagnetic layer thickness was discussed in the context of the layer potentials. The reported results confirm that the interface monolayers play a dominant role in the intrinsic GMR.