Question

Steven is making a scrapbook using 15 photos and 12 newspaper clippings. He wants all the pages to be set up in the same way, with the same combination of photos and newspaper clippings on every page. He also wants to make sure that no items are left over. What is the greatest number of scrapbook pages Steven can create?

Answer 1

To find the greatest number of scrapbook pages, we need to find the greatest common divisor of the number of photos and newspaper clippings. In this case, the GCD is 6, so Steven can create 6 pages.

Step-by-step explanation:

To determine the greatest number of scrapbook pages Steven can create, we need to find the greatest common divisor (GCD) of the number of photos and the number of newspaper clippings. The GCD represents the maximum number of pages with the same combination of items.

Given that Steven has 15 photos and 12 newspaper clippings, we can find the GCD using the prime factorization method. The prime factorization of 15 is 3 x 5, and the prime factorization of 12 is 2 x 2 x 3.

The GCD is the product of the common prime factors raised to the lowest exponent, which in this case is 2 x 3 = 6. Therefore, the greatest number of scrapbook pages Steven can create is 6.