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# Which of the following numbers has the greatest number of distinct

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Math Expert
Joined: 02 Sep 2009
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Which of the following numbers has the greatest number of distinct  [#permalink]

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13 Apr 2016, 06:12
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25% (medium)

Question Stats:

77% (02:00) correct 23% (01:49) wrong based on 181 sessions

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Which of the following numbers has the greatest number of distinct prime factors?

A. 165
B. 192
C. 228
D. 330
E. 332

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Re: Which of the following numbers has the greatest number of distinct  [#permalink]

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13 Apr 2016, 06:28
165=3*5*11
192=2^6 *3
228=2^2 *3*19
330=2*3*5*11
332=2^2 * 83

330 has 4 distinct prime factors
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Re: Which of the following numbers has the greatest number of distinct  [#permalink]

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14 May 2017, 05:31
is trial and error the only way to solve this, or is there a trick to eliminate the obvious ones?
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Re: Which of the following numbers has the greatest number of distinct  [#permalink]

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14 May 2017, 05:34
ameyaprabhu wrote:
is trial and error the only way to solve this, or is there a trick to eliminate the obvious ones?

Yes, you should do prime factorization to get the answer.
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Re: Which of the following numbers has the greatest number of distinct  [#permalink]

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18 May 2017, 20:01
Bunuel wrote:
Which of the following numbers has the greatest number of distinct prime factors?

A. 165
B. 192
C. 228
D. 330
E. 332

We can express each answer choice as a product of its prime factors:

A) 165

165 = 5 x 33 = 5 x 11 x 3

165 has 3 distinct prime factors.

B) 192

192 = 8 x 24 = 8 x 8 x 3 = 2^6 x 3^1

192 has 2 distinct prime factors.

C) 228

228 = 4 x 57 = 2^2 x 57

228 has 2 distinct prime factors.

D) 330

330 = 10 x 33 = 2 x 3 x 5 x 11

330 has 4 distinct prime factors.

E) 332

332 = 4 x 83 = 2^2 x 83

332 has 2 distinct prime factors.

330 has the greatest number of distinct prime factors.

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Re: Which of the following numbers has the greatest number of distinct  [#permalink]

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04 Jul 2017, 07:20
Bunuel wrote:
ameyaprabhu wrote:
is trial and error the only way to solve this, or is there a trick to eliminate the obvious ones?

Yes, you should do prime factorization to get the answer.

Bunuel mean there is no way out except applying factroization on every question it is taking time it took my 2 minutes
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Re: Which of the following numbers has the greatest number of distinct  [#permalink]

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26 Nov 2018, 18:38
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Re: Which of the following numbers has the greatest number of distinct   [#permalink] 26 Nov 2018, 18:38
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