An aggregation exercise is proposed that aims at investigating whether the fast average adjustment of the disaggregate inflation series of the euro-area CPI translates into the slow adjustment of euro-area aggregate inflation. We first estimate a dynamic factor model for 404 inflation sub-indices of the euro area CPI. This allows to decompose the dynamics of inflation sub-indices in two parts: one due to a common "macroeconomic" shock and one due to sector specific "idiosyncratic" shocks. Although "idiosyncratic" shocks dominate the variance of sectoral prices, one common factor, which accounts for 30 per cent of the overall variance of the 404 disaggregate inflation series, is the main driver of aggregate dynamics. In addition, the heterogenous propagation of this common shock across sectoral inflation rates, and in particular its slow propagation to inflation rates of services, generates the persistence of aggregate inflation. We conclude that the aggregation process explains a fair amount of aggregate inflation persistence.