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# For positive integers a, b, and c, where a<b<c, the product abc has ex

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Re: For positive integers a, b, and c, where a<b<c, the product abc has ex [#permalink]
Bunuel wrote:
For positive integers a, b, and c, where a<b<c, the product abc has exactly three prime factors. What is the maximum number of prime factors of a?

A. 0
B. 1
C. 2
D. 3
E. 4

Hi GMATPrepNow,

Can you throw some light on these kinds of problem?

The easiest way to deal?
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Re: For positive integers a, b, and c, where a<b<c, the product abc has ex [#permalink]
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Option D

Number of prime factors of a will be maximum when a has same prime factors as the product a*b*c.
So, the maximum number of prime factors a can have = number of prime factors of product a*b*c = 3.
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Re: For positive integers a, b, and c, where a<b<c, the product abc has ex [#permalink]
Nice trap question.

The product result has exactly three prime factors.

The question doesn’t say that one prime factor comes from each number, the 3 prime factors can be present in all three value of A < B < C

A = (2) (3) (5)

B = (2)^2 (3)^2 (5)

C = (2)^3 (3)^3 (5)

Result of multiplication:

ABC = (2)^6 * (3)^6 * (5)^3

Condition is met- Result of ABC is divisible by exactly 3 prime factors 2, 3, and 5

And A can have all 3 prime factors

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Re: For positive integers a, b, and c, where a<b<c, the product abc has ex [#permalink]
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Re: For positive integers a, b, and c, where a<b<c, the product abc has ex [#permalink]
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