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Although aneuploidy is found in the majority of tumors, the degree of aneuploidy varies widely. It is unclear how cancer cells become aneuploid or how highly aneuploid tumors are different from those of more normal ploidy. We developed a simple computational method that measures the degree of aneuploidy or structural rearrangements of large chromosome regions of 522 human breast tumors from The Cancer Genome Atlas (TCGA). Highly aneuploid tumors overexpress activators of mitotic transcription and the genes encoding proteins that segregate chromosomes. Overexpression of three mitotic transcriptional regulators, E2F1, MYBL2, and FOXM1, is sufficient to increase the rate of lagging anaphase chromosomes in a non-transformed vertebrate tissue, demonstrating that this event can initiate aneuploidy. Highly aneuploid human breast tumors are also enriched in TP53 mutations. TP53 mutations co-associate with the overexpression of mitotic transcriptional activators, suggesting that these events work together to provide fitness to breast tumors.