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Largest prime factor

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Largest prime factor [#permalink] New post 16 Jan 2018, 12:00
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Question Stats:

85% (00:55) correct 15% (00:18) wrong based on 20 sessions



Quantity A
Quantity B
Largest prime factor of 1,728
7


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: Large prime factor [#permalink] New post 26 Jan 2018, 13:41
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I'm assuming the problem is supposed to say "largest" rather than "large." Anyway, nearly every time a problem talks about factors, or divisibility, a good first thought is to factor out the number down to its primes. I would first see whether the number meant anything to me. For example, if in this problem, quantity A said "343", I would recognize that as 7 cubed and thus the answer would be C. This is why it's a good idea to study the squares, cubes, and powers.
In this problem though, the number 1,728 doesn't mean anything to me, so I'll have to break it down to its primes. Now, 1,728 may seem pretty large but it'll go pretty quickly. I'd divide by 2 every time first because it's the easiest to divide by:
1,728 --> 2x864 --> 2x2x432 --> 2x2x2x216 --> 2x2x2x2x108 (at this point I recognize that 108 is 27x4, and the largest prime factor of 27 is 3, but if you don't recognize 108, just keep going until you recognize the number) --> 2x2x2x2x2x54 --> 2x2x2x2x2x2x27 --> a bunch of 2s and three 3s.
Therefore, the largest prime of 1,728 is 3 and the answer is B.
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Re: Largest prime factor [#permalink] New post 10 Feb 2018, 08:17
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Expert's post
Carcass wrote:



Quantity A
Quantity B
Largest prime factor of 1,728
7



This requires some prime factorization

1728 = (2)(2)(2)(2)(2)(2)(3)(3)(3)
The largest prime factor is 3

So, we get:
Quantity A: 3
Quantity B: 7

Answer: B


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Re: Largest prime factor [#permalink] New post 11 Mar 2018, 07:18
This requires some prime factorization

1728 = (2)(2)(2)(2)(2)(2)(3)(3)(3)
The largest prime factor is 3

So, we get:
Quantity A: 3
Quantity B: 7

Answer: B
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Re: Largest prime factor [#permalink] New post 12 Mar 2018, 01:22
B
Re: Largest prime factor   [#permalink] 12 Mar 2018, 01:22
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