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The greatest common factor (GCF) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To find the GCF of 250 and 750, we first list the factors of each number. The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250. The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, and 750. The GCF of 250 and 750 is 250, as it is the largest number that appears in both lists.