Miranda has just moved to a new town and wants to share plates of baked goods with her neighbors. She has 12 cookies and 18 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates she can make to share?
Question
Miranda has just moved to a new town and wants to share plates of baked goods with her neighbors. She has 12 cookies and 18 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates she can make to share?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of cookies and brownies, as this will give us the maximum number of plates Miranda can make with an equal number of each baked good and no leftovers.
Step 1: List the divisors of each number. The divisors of 12 are: 1, 2, 3, 4, 6, 12. The divisors of 18 are: 1, 2, 3, 6, 9, 18.
Step 2: Identify the common divisors. The common divisors of 12 and 18 are: 1, 2, 3, 6.
Step 3: The greatest common divisor is the largest of these, which is 6.
So, Miranda can make 6 plates to share with her neighbors.
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