Integers mod n

Puzzle Instructions:
Use the dropdown menu below to create an m by n array then use clicks to color each column a different color.
In Row 1, click on a cell to change its colors.
If it is labeled 2 click on it 2 times. If is labeled 3 click on it 3 times. 

In Row 2, if the cell is labeled 10, click on it 10 times. What color is the cell?

Now make a different shaped rectangular grid and color code those columns.  What do you notice? 

If your rectangle is 3 by 5, how many times do you need to click on each cell in column 2 to make them the same color?

If your rectangle is 4 by 7, how many times do you need to click on the cell labeled 25, to make it the correct color?