A patio is to be built with 160 tiles. In how many different rectangular arrays can it be arranged

Question

A patio is to be built with 160 tiles. In how many different rectangular arrays can it be arranged

Answer 1

We are only dealing with a rectangular pattern.

I assume we are not planning on cutting any of the tiles

so we are only working with full 160 pieces.

 

Let's factor out 160

 

                      160                    1)  160 by 1

                   

                     2  *  80               2) 2 by 80

                

                 2  * 2  *  40            3) 4 by 40

       

              2 * 2 * 2 * 20            4) 8 by 20

 

          2  *  2  * 2  * 2  * 10     5)  16 by 10

       

        2 * 2 * 2 * 2 * 2 * 5        6)  32 by 5

 

This is as far down as you can break 160.

There are 6 possible rectangular combinations.