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Tanvi is making a scrapbook using 40 photos and 28 newspaper clippings. She wants all the pages to be set up in the same way, with the same combination of photos and newspaper clippings on every page. She also wants to make sure that no items are left over. What is the greatest number of scrapbook pages Tanvi can create? pages

Question

Tanvi is making a scrapbook using 40 photos and 28 newspaper clippings. She wants all the pages to be set up in the same way, with the same combination of photos and newspaper clippings on every page. She also wants to make sure that no items are left over. What is the greatest number of scrapbook pages Tanvi can create? pages

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the number of photos (40) and the number of newspaper clippings (28). The GCD is the largest number that divides both numbers without leaving a remainder.

Here are the steps to find the GCD:

  1. List the prime factors of each number:

    • Prime factors of 40: 2, 2, 2, 5
    • Prime factors of 28: 2, 2, 7

  2. Identify the common prime factors:

    • The common prime factors are 2 and 2.

  3. Multiply the common prime factors together to find the GCD:

    • GCD = 2 * 2 = 4

So, the greatest number of scrapbook pages Tanvi can create is 4.

This problem has been solved

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