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Azimuthal dihadron correlations of charged particles have been measured in PbPb collisions at √sNN = 2.76 TeV byCMS Collaboration, using data from the 2011 LHC heavy-ion run. The data set includes a sample of ultra-central (0–0.2% centrality) PbPb events collected using a trigger based on total transverse energy in the hadron forward calorimeters and the total multiplicity of pixel clusters in the silicon pixel tracker. A total of about 1.8 million ultra-central events were recorded, corresponding to an integrated luminosity of 120 μb−1. The observed correlations in ultra-central PbPb events are expected to be particularly sensitive to initial-state fluctuations. The single-particle anisotropy Fourier harmonics, from v2 to v6, are extracted as a function of particle transverse momentum. At higher transverse momentum, the v2 harmonic becomes significantly smaller than the higher-order vn (n ≥ 3). The pT-averaged v2 and v3 are found to be equal within 2%, while higher-order vn decrease as n increases. The breakdown of factorization of dihadron correlations into single-particle azimuthal anisotropies is observed. This effect is found to be most prominent in the ultra-central PbPb collisions, where the initial-state fluctuations play a dominant role. A comparison of the factorization data to hydrodynamic predictions with event-by-event fluctuating initial conditions is also presented.