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Aubrey is decorating papers with a total of 12 heart stickers and 16 star stickers for the child she is babysitting. If she wants to make all the papers identical, with the same combination of heart and star stickers and no stickers left over, what is the greatest number of pages Aubrey can decorate?

Question

Aubrey is decorating papers with a total of 12 heart stickers and 16 star stickers for the child she is babysitting. If she wants to make all the papers identical, with the same combination of heart and star stickers and no stickers left over, what is the greatest number of pages Aubrey can decorate?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the number of heart stickers (12) and the number of star stickers (16). The GCD is the largest number that divides both numbers without leaving a remainder.

Here are the steps to find the GCD of 12 and 16:

  1. List the prime factors of each number:

    • The prime factors of 12 are 2, 2, and 3.
    • The prime factors of 16 are 2, 2, 2, and 2.

  2. Identify the common prime factors:

    • The common prime factors are 2 and 2.

  3. Multiply the common prime factors together:

    • 2 * 2 = 4.

So, the GCD of 12 and 16 is 4.

This means that Aubrey can decorate a maximum of 4 pages, with each page having the same combination of heart and star stickers and no stickers left over.

This problem has been solved

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