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Reagan is setting out Japanese food for a party she is having. She has 30 avocado rolls and 24 cucumber rolls. If she wants each plate to be identical, with no rolls left over, what is the greatest number of platters Reagan can create?

Question

Reagan is setting out Japanese food for a party she is having. She has 30 avocado rolls and 24 cucumber rolls. If she wants each plate to be identical, with no rolls left over, what is the greatest number of platters Reagan can create?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 30 (avocado rolls) and 24 (cucumber rolls). 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 30 are 2, 3, and 5.
    • The prime factors of 24 are 2, 2, 2, and 3.

  2. Identify the common prime factors:

    • The common prime factors are 2 and 3.

  3. Multiply the common prime factors together:

    • 2 * 3 = 6

So, the greatest number of identical platters Reagan can create is 6.

This problem has been solved

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