Quantifying the number of selective sweeps and their combined effects on genomic diversity in humans and other great apes is notoriously difficult. Here we address the question using a comparative approach to contrast diversity patterns according to the distance from genes in all great ape taxa. The extent of diversity reduction near genes compared with the rest of intergenic sequences is greater in a species with larger effective population size. Also, the maximum distance from genes at which the diversity reduction is observed is larger in species with large effective population size. In Sumatran orangutans, the overall genomic diversity is ∼30% smaller than diversity levels far from genes, whereas this reduction is only 9% in humans. We show by simulation that selection against deleterious mutations in the form of background selection is not expected to cause these differences in diversity among species. Instead, selective sweeps caused by positive selection can reduce diversity level more severely in a large population if there is a higher number of selective sweeps per unit time. We discuss what can cause such a correlation, including the possibility that more frequent sweeps in larger populations are due to a shorter waiting time for the right mutations to arise.