aria is preparing dinner plates. She has 45 pieces of chicken and 15 rolls. If she wants to make all the plates identical without any food left over, what is the greatest number of plates Maria can prepare?
Question
aria is preparing dinner plates. She has 45 pieces of chicken and 15 rolls. If she wants to make all the plates identical without any food left over, what is the greatest number of plates Maria can prepare?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 45 (pieces of chicken) and 15 (rolls). The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: List the divisors of each number.
The divisors of 45 are: 1, 3, 5, 9, 15, 45. The divisors of 15 are: 1, 3, 5, 15.
Step 2: Identify the common divisors.
The common divisors are: 1, 3, 5, 15.
Step 3: The greatest common divisor is the largest of these, which is 15.
So, Maria can prepare 15 plates, each with 3 pieces of chicken and 1 roll.
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