Luke 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 combination of math and science books, with no books left over, what is the greatest number of bookshelves Luke can use?
Question
Luke 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 combination of math and science books, with no books left over, what is the greatest number of bookshelves Luke can use?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of math books and science books. The GCD is the largest number that can divide both numbers without leaving a remainder.
Here are the steps:
- List the divisors of 9: 1, 3, 9
- List the divisors of 12: 1, 2, 3, 4, 6, 12
- Identify the common divisors: 1, 3
- The greatest common divisor is 3.
Therefore, the greatest number of bookshelves Luke can use to distribute his books evenly is 3.
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