Higher Order Thinking Mr. Deets is making an array to display 9 pictures. For each pair of different factors, there are two arrays he can make. How many different arrays can Mr. Deets make? Is the number of arrays odd or even? Explain.

To determine how many different arrays Mr. Deets can make with 9 pictures, we first find the factor pairs of 9. The factors of 9 are 1, 3, and 9. The possible pairs are (1, 9) and (3, 3). Each pair has two arrangements (e.g., for the pair (1, 9), one array can be 1 row with 9 columns, and the other can be 9 rows with 1 column). Since (3, 3) is a square array and only allows one distinct arrangement, we only count the two arrangements from the (1, 9) pair along with the one from (3, 3). Thus, Mr. Deets can create 2 + 1 = 3 arrays in total. Since 3 is odd, Mr. Deets can make an odd number of different arrays. So, Mr. Deets is quite the picture organizer! While he has three creative arrangements in his arsenal, he can feel pretty special for having an odd number of unique ways to display his artwork, making it all the more fun and quirky!