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Re: Company H distributed $4,000 and 180 pencils evenly among it [#permalink]
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sandy wrote:
Company H distributed $4,000 and 180 pencils evenly among its employees, with each employee getting an equal integer number of dollars and an equal integer number of pencils. What is the greatest number of employees that could work for company H?

(A) 9
(B) 10
(C) 20
(D) 40
(E) 180


Another way to state this question is: What is the greatest common divisor of 4000 and 180?

You can answer this question by finding the prime factorization of 4000 and 180

4000 = (2)(2)(2)(2)(2)(5)(5)(5)
180 = (2)(2)(3)(3)(5)

The two numbers have two 2's in common and one 5 in common.

So the greatest common divisor = (2)(2)(5) = 20

Answer: C

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Re: Company H distributed $4,000 and 180 pencils evenly among it [#permalink]
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Given that a company has distributed $4000 and 180 pencils evenly on its employees.
Asking what is the greatest number who could work at the company.

In other words, we need to find the greatest common divisor of 4000 and 180.
4000 = 2^5*5^3
180= 3^2*2^2*5
GCF = 2^2*5 = 20 answer C.

Or different approach, divide 4000 and 180 by each answer choice.
the answer must give solution that can't be simplify further.
C. 20 = 4000/20 =200 and 180/20 = 9
since 200 and 9 can't be simplified more, 20 is gcf of 4000 and 180.
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Re: Company H distributed $4,000 and 180 pencils evenly among it [#permalink]
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