In preparation for a party, Miguel is putting desserts onto platters. The chocolate cake is cut into 51 pieces and the cheesecake is cut into 85 pieces. If he wants to prepare identical platters without having any cake left over, what is the greatest number of platters he can prepare?
Question
In preparation for a party, Miguel is putting desserts onto platters. The chocolate cake is cut into 51 pieces and the cheesecake is cut into 85 pieces. If he wants to prepare identical platters without having any cake left over, what is the greatest number of platters he can prepare?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of chocolate cake pieces (51) and the number of cheesecake pieces (85). The GCD is the largest number that divides both numbers without leaving a remainder.
Here are the steps to find the GCD:
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List the prime factors of each number:
- Prime factors of 51: 3, 17
- Prime factors of 85: 5, 17
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Identify the common prime factors: 17
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The GCD is the product of the common prime factors. In this case, the GCD is 17.
Therefore, the greatest number of identical platters Miguel can prepare without having any cake left over is 17.
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