Percy is stocking toilets at the hotel where he works. He has 24 rolls of toilet paper and 28 soaps. If he wants all toilets to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest number of toilets Percy can stock?
Question
Percy is stocking toilets at the hotel where he works. He has 24 rolls of toilet paper and 28 soaps. If he wants all toilets to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest number of toilets Percy can stock?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 24 (toilet paper rolls) and 28 (soaps). The GCD is the largest number that divides both numbers without leaving a remainder.
Here are the steps to find the GCD of 24 and 28:
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List the prime factors of each number:
- Prime factors of 24: 2, 2, 2, 3
- Prime factors of 28: 2, 2, 7
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Identify the common prime factors:
- The common prime factors are 2 and 2.
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Multiply the common prime factors together:
- 2 * 2 = 4
So, the GCD of 24 and 28 is 4.
This means that Percy can stock 4 toilets identically with the same combination of supplies in each one and nothing left over.
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