The greatest common factor of 45 and 72 is 9 because the factors of 45 is 1, 2, 3, 5, 9, 15, 45. And the factors of 72 is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. The greatest commen factor is the factor that is the greatest and is the same in both of the sets of factors. 1 is a factor between them but it is not the greatest, not 2 or 3, but it is 9 because it is the greatest and each set has 9. Thank you for asking, have a great afternoon :)