A data-driven method was applied to Au+Au collisions at sNN=200GeV made with the STAR detector at RHIC to isolate pseudorapidity distance δη-dependent and δη-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a δη-independent component of the correlation, which is dominated by anisotropic flow and flow fluctuations. It was also found to be independent of η within the measured range of pseudorapidity |η|<1. In 20-30% central Au+Au collisions, the relative flow fluctuation was found to be 34%±2%(stat.)±3%(sys.) for particles with transverse momentum pT less than 2 GeV/c. The δη-dependent part, attributed to nonflow correlations, is found to be 5%±2%(sys.) relative to the flow of the measured second harmonic cumulant at |δη|>0.7.