Andy has 9 math books and 6 reading books if you wants to distribute them evenly among some bookshelves so that each has the same combination of books with none left over what is the greatest number of bookshelves Andy can use

9 math books

6 reading books

First we need to find the greatest common factor.

in this case it would be 3.

9 : 3 = 3

6 : 3 = 2

Here we have our answer

since 3 is not an even number it cannot be split evenly which means each bookcase will have at least 3 math books on it - and 2 reading books as well

*bookcase 1:

3 (math)

2 (reading

*bookcase 2:

3 (math)

2 (reading)

*bookcase 3:

3 (math)

2 (reading

3 is the greatest number of book shelves Andy can use. I solved this by finding the greatest comment factor of 9 and 6, which turned out to be 3.

6/3=2 (reading books per shelf)

9/3=3 (math books per shelf)

Every shelf there are two reading books and 3 math books