32 mystery books and 56 biography books, each shelf has the same number of books on them, how many books go on each shelf and how many shelves for each type of book

8 books

4 mystery shelves and 7 biography shelves

Step-by-step explanation:

To arrive at each figure, the multiples of 32 and 56 are

32=2*2*2*2*2

56=2*2*2*7

You notice that each term hss 2*2*2=8 hence the number of books per shelf is 8

Since mystery books are 32 and a shelf has 8 books then the number of shelves will be 32/8 = 4 shelves. Similarly, for biography books, the number of shelves will be 56/8 = 7 shelves