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To find the greatest common factor (GCF) of 14m^2 and 21m, we first need to factor each term. The factors of 14m^2 are 1, 2, 7, 14, m, and m. The factors of 21m are 1, 3, 7, 21, m, and 1. The common factors between the two terms are 1, 7, and m. Therefore, the greatest common factor of 14m^2 and 21m is 7m.
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