Determining the number of factors in exploratory factor analysis (EFA) is crucial because it affects the rest of the analysis and the conclusions of the study. Researchers have developed various methods for deciding the number of factors to retain in EFA, but this remains one of the most difficult decisions in the EFA. The purpose of this study is to compare the parallel analysis with the performance of fit indices that researchers have started using as another strategy for determining the optimal number of factors in EFA. The Monte Carlo simulation was conducted with ordered categorical items because there are mixed results in previous simulation studies, and ordered categorical items are common in behavioral science. The results of this study indicate that the parallel analysis and the root mean square error of approximation (RMSEA) performed well in most conditions, followed by the Tucker-Lewis index (TLI) and then by the comparative fit index (CFI). The robust corrections of CFI, TLI, and RMSEA performed better in detecting misfit underfactored models than the original fit indices. However, they did not produce satisfactory results in dichotomous data with a small sample size. Implications, limitations of this study, and future research directions are discussed.