The validity of (1-q) expansion and factorization approximations are analysed in the framework of Tsallis statistics. We employ exact expressions for classical independent systems (harmonic oscillators) by considering the unnormalized and normalized constrainsts. We show that these approxiamtions can not be accurate in the analysis of systems with many degrees of freedom. I-IntroductionEver since the presentation by Tsallis[1, 2, 3] of a new possible generalization of the statistical mechanics (Tsallis statistics) based on the nonextensive entropy,a large number of investigations has been developed concerning this subject [4]. These investigations are basically employed in the discussion of aspects related to nonextensive phenomena, such as, Lévy-type anomalous superdiffusion [5], Euler turbulence[6], self-gravitating systems and related themes [6,7,8,9,10], cosmic background radiation [11,12,13,14] [11,13,14] and in other many independent particle systems [27,28,29,30,31,32], but without a careful analysis of the validity of these methods. Thus, a detailed discussion of the (1 − q) expansion and the factorization approximation plays a special role in this scenario. In this direction, Ref.[33] contains a discussion comparing these approximations in the context of the quantum gases. However, some important aspects of the comparison are still lacking, in particular the importance of the degrees of freedom N . This work is addressed to analyze how precise the (1−q) expansion and the factorization approximation are by considering N arbitrary. To perform this study it is convenient to consider a solvable model in order to carefully understand the degree of accuracy of these approximations. Furthermore, the chosen model must contain important features of other more realistic ones. This is just the case of a set of harmonic oscillators.In this direction, to analyze the (1 − q) expansion and the factorization approximation, we focus our discussion on the classical Tsallis statistics by considering N one dimesional harmonic oscillators, i. e., we employ the Hamiltonian H =