A class of 23 students was using square tiles to build rectangular shapes. Each student has more than one tile and each has a different number of tiles. Each student was able to build only one rectangular shape. All tiles had to be used to build the rectangle and the rectangle could have no holes. For example, a 2 by 6 rectangle uses 12 tiles and is considered 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 rectangles. How many tiles did the class require?

Question

A class of 23 students was using square tiles to build rectangular shapes.  Each student has more than one tile and each has a different number of tiles.  Each student was able to build only one rectangular shape.  All tiles had to be used to build the rectangle and the rectangle could have no holes.  For example, a 2 by 6 rectangle uses 12 tiles and is considered 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 rectangles.  How many tiles did the class require?