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Re: Company H distributed $4,000 and 180 pencils evenly among it
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15 Aug 2018, 05:17
Explanation
In order to distribute $4,000 and 180 pencils evenly, the number of employees must be a factor of each of these two numbers. Because the question asks for the greatest number of employees possible, start by checking the greatest choices:
(E) $4,000 could not be evenly distributed among 180 employees (although 180 pencils could).
(D) $4,000 could be evenly divided among 40 people, but 180 pencils could not.
(C) is the greatest choice that works—$4,000 and 180 pencils could each be evenly distributed among 20 people.
Alternatively, find the greatest common factor (GCF) of the two numbers. Factor: \(4,000 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 = 2^5 \times 5^3\) and \(180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5\). These numbers have 2 × 2 × 5 in common, so 20 is the GCF.