You need to calculate the common divisors of both numbers 24 and 16. To do that, factor each number: 24 = 2*2*2*3 and 16 = 2*2*2*2. That means that the common divisors are 2, 2^2 = 4 and 2^3 = 8. Start by using 2 shelves: each of them will have 24/2 = 12 novels and 16/2 = 8 autobiographies. Now use 4 shelves: each shelf will have 24/4 = 6 novels and 16/4 = 4 autobiographies per shelf. Use 8 shelves: 24/8 = 3 novels per shelf and 16/8 = 2 autobiographies per shelf. Of course, he can use just 1 shelf (1 is a divisor of any number) with all the books. So, the answer is tha the possible numbers of shelves Carlos will use is: 1, 2, 4, and 8.
