list the pairs of factors of 24
1x24
2x12
etc.
1x24
2x12
etc.
Let's start by finding all the factors of 24. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Since we are looking for rectangular arrays, we can pair up these factors to form pairs of length and width. For example, (1, 24), (2, 12), (3, 8), and (4, 6).
For each pair, we can create a rectangular array by placing the squares in the desired configuration. For instance, for (1, 24), the array would have 1 row and 24 columns, for (2, 12), it would have 2 rows and 12 columns, and so on.
Let's list all the possible arrays:
(1, 24) -> 1 row, 24 columns
(2, 12) -> 2 rows, 12 columns
(3, 8) -> 3 rows, 8 columns
(4, 6) -> 4 rows, 6 columns
(6, 4) -> 6 rows, 4 columns
(8, 3) -> 8 rows, 3 columns
(12, 2) -> 12 rows, 2 columns
(24, 1) -> 24 rows, 1 column
Thus, there are 8 different arrays for modeling a rectangular quilt with 24 paper squares.