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Brian has collected 18 T-shirts and 12 buttons from his favorite band. He wants to combine them into identical sets to sell, with no pieces left over. What is the greatest number of sets Brian can make?

Question

Brian has collected 18 T-shirts and 12 buttons from his favorite band. He wants to combine them into identical sets to sell, with no pieces left over. What is the greatest number of sets Brian can make?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the number of T-shirts (18) and the number of buttons (12). The GCD is the largest number that can divide both numbers without leaving a remainder.

Here are the steps to find the GCD:

  1. List the prime factors of each number:

    • The prime factors of 18 are 2, 3, 3.
    • The prime factors of 12 are 2, 2, 3.

  2. Identify the common prime factors:

    • The common prime factors are 2 and 3.

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

    • 2 * 3 = 6.

So, the greatest number of sets Brian can make is 6. Each set will contain 3 T-shirts and 2 buttons.

This problem has been solved

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