A class of 23 students was using square tiles to build rectangular shapes. Each student had more than 1 tile and each had a different number of tiles. Each student was able to build only one shape of rectangle. All tiles had to be used to build a rectangle and the rectangle could not have holes. For example, a 2 by 6 uses 12 tiles and is consisted the same as a 6 by 2 rectangle but is different from a 3 by 4 rectangle. The class did the activity using the least number of tiles. How many tiles did the class use? Explore the various rectangles that could be made.

To find the number of tiles the class used, we need to consider all possible rectangle shapes that can be constructed using square tiles with the given conditions.

Let's start by finding all possible pairs of factors of 23. Since each student had a different number of tiles, we need to exclude perfect square factors.

The factors of 23 are 1 and 23.

Next, we need to find all possible rectangles that can be formed using these factors.

Case 1: 1 by 23
In this case, the rectangle would have dimensions of 1 by 23. Since the rectangle cannot have holes, the class would need a total of 23 tiles.

Case 2: 23 by 1
In this case, the rectangle would have dimensions of 23 by 1. Once again, the class would need a total of 23 tiles.

So, the class would use a total of 23 tiles in either case.

Therefore, the class used 23 tiles in total.

To find out how many tiles the class used, we need to consider the possible arrangements of the tiles to form rectangles. Let's start by listing all the possible factors of 23, since each student had a different number of tiles:

1, 23

Since 23 is a prime number, these are the only possible factors. Now, let's see what rectangles can be formed using these factors.

For 1 tile:
1 by 23

For 23 tiles:
23 by 1

These are the only possible rectangles that can be formed using the given factors.

Now, we need to find which of these rectangles uses the least number of tiles. Both options use 23 tiles, so the class used a total of 23 tiles.

In summary, the class used a total of 23 tiles and the possible rectangles that can be formed are a 1 by 23 rectangle and a 23 by 1 rectangle.