Using the greatest common factor, it is found that 5 books will be on each shelf.
How to find how many books will be on each shelf?
Mr. Yaws has:
Each shelf will have either all nonfiction books or all fiction books. They also contain the same number of books, which is the greatest possible. Hence, this number is the greatest common factor of 20 and 15.
This greatest common factor is found factoring both numbers by prime factors simultaneously, hence:
20 - 15|5
5 - 3
Hence:
gcf(20,15) = 5.
Which means that 5 books will be on each shelf.
More can be learned about the greatest common factor at https://brainly.com/question/6032811
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