Differential measurements of charged particle azimuthal anisotropy are presented for lead-lead collisions at √s_(NN)=2.76 TeV with the ATLAS detector at the LHC, based on an integrated luminosity of approximately 8 μb^(−1). This anisotropy is characterized via a Fourier expansion of the distribution of charged particles in azimuthal angle relative to the reaction plane, with the coefficients v_n denoting the magnitude of the anisotropy. Significant v_2–v_6 values are obtained as a function of transverse momentum (0.52) and one particle with p_T<3 GeV, the v_(2,2)–v_(6,6) values are found to factorize as v_(n,n)(p_T^a,p_T^b)≈v_n(p_T^a)v_n(p_T^b) in central and midcentral events. Such factorization suggests that these values of v_(2,2)–v_(6,6) are primarily attributable to the response of the created matter to the fluctuations in the geometry of the initial state. A detailed study shows that the v_(1,1)(p_T^a,p_T^b) data are consistent with the combined contributions from a rapidity-even v_1 and global momentum conservation. A two-component fit is used to extract the v_1 contribution. The extracted v_1 is observed to cross zero at p_T≈1.0 GeV, reaches a maximum at 4–5 GeV with a value comparable to that for v_3, and decreases at higher p_T
