The factors of 60 are 60, 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, 1.The factors of 75 are 75, 25, 15, 5, 3, 1.The common factors of 60 and 75 are 15, 5, 3, 1, intersecting the two sets above.In the intersection factors of 60 ∩ factors of 75 the greatest element is 15.Therefore, the greatest common factor of 60 and 75 is 15.