How many books in each stack?

Question

A college bookstore has 16 blue books and 24 red books. If they want to display the books with the same number in each stack and only one color in each stack, what is the largest number of books in each stack?

Answer 1

Find the largest common factor of the numbers of blue and red books, and distribute the books into stacks with that number of books (of the same color) per stack.

 

There are 16 blue books.

 

16 = 2⁴ = 2 x 2³

 

There are 24 red books.

 

24 = 3 x 2³

 

The largest common factor of 16 and 24 is 2³ = 8.  Distribute the books into stacks of 8:

 

2 stacks of blue books, 8 books per stack

3 stacks of red books, 8 books per stack