Direct reprogramming of somatic cells into induced pluripotent stem (iPS) cells can be achieved by overexpression of Oct4, Sox2, Klf4 and c-Myc transcription factors, but only a minority of donor somatic cells can be reprogrammed to pluripotency. Here we demonstrate that reprogramming by these transcription factors is a continuous stochastic process where almost all mouse donor cells eventually give rise to iPS cells on continued growth and transcription factor expression. Additional inhibition of the p53/p21 pathway or overexpression of Lin28 increased the cell division rate and resulted in an accelerated kinetics of iPS cell formation that was directly proportional to the increase in cell proliferation. In contrast, Nanog overexpression accelerated reprogramming in a predominantly cell-division-rate-independent manner. Quantitative analyses define distinct cell-division-rate-dependent and -independent modes for accelerating the stochastic course of reprogramming, and suggest that the number of cell divisions is a key parameter driving epigenetic reprogramming to pluripotency.