Mobile traffic data collected by network operators is a rich source of information about human habits, and its analysis provides insights relevant to many fields, including urbanism, transportation, sociology and networking. In this paper, we present an original approach to infer both spatial and temporal structures hidden in the mobile demand, via a first-time tailoring of Exploratory Factor Analysis (EFA) techniques to the context of mobile traffic datasets. Casting our approach to the time or space dimensions of such datasets allows solving different problems in mobile traffic analysis, i.e., network activity profiling and land use detection, respectively. Tests with real-world mobile traffic datasets show that, in both its variants above, the proposed approach (i) yields results whose quality matches or exceeds that of state-of-the-art solutions, and (ii) provides additional joint spatiotemporal knowledge that is critical to result interpretation.