The prime factorizations of 54 and 72 are shown below. Prime factorization of 54: 2, 3, 3, 3 Prime factorization of 72: 2, 2, 2, 3, 3 Using the prime factorizations, what is the greatest common factor of 54 and 72? 2 ´ 3 2 ´ 3 ´ 3 2 ´ 2 ´ 3 ´ 3 2 ´ 2 ´ 2 ´ 3 ´ 3 ´ 3

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.