Gavin has 9 math books and 12 science books. If he wants to Distribute them evenly among some bookshelves so that each bookshelf has the same number of math and science books, with no books left over, what is the greatest number of bookshelves Gavin can use?

Answer 1

To find the maximum number of bookshelves Gavin can use while distributing his 9 math books and 12 science books evenly, we need to determine the greatest common divisor (GCD) of the two quantities.

First, we will find the GCD of 9 and 12. We can do this by listing the divisors of each number:

• The divisors of 9 are: 1, 3, 9
• The divisors of 12 are: 1, 2, 3, 4, 6, 12

The common divisors of 9 and 12 are: 1 and 3. The greatest of these is 3.

Now, let's verify that Gavin can distribute both types of books evenly across 3 bookshelves:

1. For the math books: \[ \frac{9 \text{ math books}}{3 \text{ bookshelves}} = 3 \text{ math books per bookshelf} \]

2. For the science books: \[ \frac{12 \text{ science books}}{3 \text{ bookshelves}} = 4 \text{ science books per bookshelf} \]

Since both calculations result in whole numbers, Gavin can indeed use 3 bookshelves, each containing exactly 3 math books and 4 science books.

Thus, the greatest number of bookshelves Gavin can use is \(\boxed{3}\).