This paper considers multiple changes in the factor loadings of a high dimensional factor model occurring at dates that are unknown but common to all subjects. Since the factors are unobservable, the problem is converted to estimating and testing structural changes in the second moments of the pseudo factors. This study considers both joint and sequential estimation of the change points and show that the distance between the estimated and the true change points is Op(1). It finds that the estimation error contained in the estimated pseudo factors has no effect on the asymptotic properties of the estimated change points as the cross-sectional dimension N and the time dimension T go to infinity jointly. No N-T ratio condition is needed. The study also propose (i) tests for no change versus l changes (ii) tests for l changes versus l+1 changes, and show that using estimated factors asymptotically has no effect on their limit distributions if√T/N→0. These tests allow the authors to make inference on the presence and number of structural changes. Simulation results show good performance of the proposed procedure. In an application to U.S. quarterly macroeconomic data we detect two possible breaks.