We present high-precision measurements of elliptic, triangular, and quadrangular flow v2, v3, and v4, respectively, at midrapidity for identified hadrons π, p, K, φ, Ks, Λ as a function of centrality and transverse momentum in Au+Au collisions at the center-of-mass energy √sNN=200 GeV. We observe similar vn trends between light and strange mesons which indicates that the heavier strange quarks flow as strongly as the lighter up and down quarks. The number-of-constituent-quark scaling for v2, v3, and v4 is found to hold within statistical uncertainty for 0–10%, 10–40%, and 40–80% collision centrality intervals. The results are compared to several viscous hydrodynamic calculations with varying initial conditions, and could serve as an additional constraint to the development of hydrodynamic models.