Cora is stocking bathrooms at the hotel where she works. She has 16 rolls of toilet paper and 32 soaps. If she wants all bathrooms to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest number of bathrooms Cora can stock?
Question
Cora is stocking bathrooms at the hotel where she works. She has 16 rolls of toilet paper and 32 soaps. If she wants all bathrooms to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest number of bathrooms Cora can stock?
Solution
To find the greatest number of bathrooms Cora can stock, we need to find the greatest common divisor (GCD) of the number of toilet paper rolls and soaps. 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 16 are: 1, 2, 4, 8, 16. The divisors of 32 are: 1, 2, 4, 8, 16, 32.
Step 2: Identify the common divisors. The common divisors are: 1, 2, 4, 8, 16.
Step 3: The greatest common divisor is the largest of these, which is 16.
So, Cora can stock 16 bathrooms with an identical combination of supplies and nothing left over.
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