The evaluation of the reduction state of CeO2 by XPS is still controversial because of the presence of more than 10 peaks in the Ce(3d) photoemission spectra due to Ce3+ and Ce4+, some of them at similar binding energies. This makes difficult conventional fitting using nonlinear least-square (NLLSF) methods with Gaussian-Lorentzian curves that require the knowledge of the number of bands. In the present work, we have tried to overcome this problem using factor analysis (FA), a method that, has been applied with success to other spectroscopic problems. In order to obtain confident results for the individual shapes of the components, (the basis for a correct quantification) we have combined target testing (TT) and iterative target transformation factor analysis (ITTFA). We have shown that the combined use of these two methods results in a more accurate evaluation (ca. +/- 2%) of the reduction state of partially reduced CeO2. The election of the "real factors" corresponding to Ce4+ and Ce3+ species is discussed in detail.