The dependence of the giant magnetoresistance (GMR) on the thickness of the Co layers in Co/Cu multilayers was investigated experimentally. The thickness of the Cu layer was held constant at tCu=19 Å, which corresponds to the second maximum of the GMR ratio oscillating dependence on tCu. The Co layer thickness was varied from 4.8 to 79.0 Å. High resolution transmission electron microscopy showed the existence of the two-dimensional artificial superstructure with defined periodicity as well as sharp and flat interfaces. From wide angle x-ray diffraction it was concluded that at Co layer thickness below 40 Å the multilayers are polycrystalline with mainly fcc lattice structure and (111) texture. In the case of thicker Co layers indications of hcp Co could be found. The GMR ratio reaches a maximum at Co layer thickness about 11 Å. It was shown that the GMR in sputtered Co/Cu multilayers is due to spin scattering at the interfaces and resistance is strongly influenced by interface scattering.