Rick likes to separate his collection of books into various groups by genre.  He has 400 books in total and proceeds to divide them into two separate equally-sized categories repeatedly until he has each book in a category with 24 other books.  How many times must he break these groups into smaller groups to accomplish this?
Rick starts with 400 books and divides them into two categories of equal size, meaning there are two categories of 400/2= <<400/2=200>>200 books.
Rick repeats this process again, dividing the 200 book categories into equal halves, leaving him with 200/2=<<200/2=100>>100 books in each.
Rick repeats this process again, dividing the 100 book categories into equal halves, leaving him with 100/2=<<100/2=50>>50 books in each.
Rick repeats this process again, dividing the 50 book categories into equal halves, leaving him with 50/2=<<50/2=25>>25 books in each.
Since Rick is looking for categories with 25 books in each, he accomplishes this by the 4th step.
#### 4