Direct reprogramming of somatic cells into induced pluripotent stem cells (iPSCs) is a stochastic process where almost all donor cells eventually give rise to iPSCs upon continued growth and transcription factor expression. Inhibition of the p53/p21 pathway or overexpression of Lin28 increases the cell division rate and accelerates iPSC formation, while overexpression of Nanog accelerates reprogramming in a cell division rate-independent manner. Quantitative analyses reveal distinct modes for accelerating the stochastic course of reprogramming, suggesting that the number of cell divisions is a key parameter driving epigenetic reprogramming to pluripotency.Direct reprogramming of somatic cells into induced pluripotent stem cells (iPSCs) is a stochastic process where almost all donor cells eventually give rise to iPSCs upon continued growth and transcription factor expression. Inhibition of the p53/p21 pathway or overexpression of Lin28 increases the cell division rate and accelerates iPSC formation, while overexpression of Nanog accelerates reprogramming in a cell division rate-independent manner. Quantitative analyses reveal distinct modes for accelerating the stochastic course of reprogramming, suggesting that the number of cell divisions is a key parameter driving epigenetic reprogramming to pluripotency.