Question

Kim needs to place 32 mystery books and 56 biography books on the library shelves. She is to place the maximum number of books on each shelf so that all the shows have the same number of books. Each shelf will contain only one type of book determine the number of books to be placed on each shelf

Answer 1

You would need to find the GCF of both 32 and 56. How you do that is you find the factors of each number:
32: 32, 16, 8, 4, 2, 1
56: 56, 28, 14, 8, 7, 4, 2, 1
Next you find all the common factors of the two numbers by intersecting the two sets of factors:
8, 4, 2, 1
Finally, you identify the greatest element of the common factors of 32 and 56 which is 8
Therefore the GCF of 32 and 56 is 8, and there would be 8 books on each shelf in the library.
Hope this helps! :)