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Ian has 1212 math books and 1818 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 Ian can use?\newline_____\_\_\_\_\_ bookshelves

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Q. Ian has 1212 math books and 1818 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 Ian can use?\newline_____\_\_\_\_\_ bookshelves
  1. Identify Problem: Identify the problem: We need to find the greatest number of bookshelves that can be used such that each shelf has the same number of math and science books without any left over.
  2. Determine Method: Determine the method: To solve this, we need to find the Greatest Common Factor (GCF) of the number of math books 1212 and science books 1818.
  3. Calculate GCF: Calculate the GCF: List the factors of 1212 (11, 22, 33, 44, 66, 1212) and 1818 (11, 22, 33, 66, 1122, 1818). The common factors are 11, 22, 33, and 66. The greatest of these is 66.
  4. Conclusion: Conclusion: Ian can use 66 bookshelves to distribute his books evenly. Each shelf will have 22 math books and 33 science books.

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