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I have three counters.  I arrange them on a grid to make a rectangle like this:

 
I wonder if there are any other rectangles I could make with just three counters?

If I had six counters, I could make a rectangle like this:



Are there any other rectangles that I could make with six counters?

Imagine you have $18$ counters to put on a grid.

Arrange any number of counters on the grid to make a rectangle (not just its outline).
How many different rectangles can you make with each number of counters?