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Which of the following numbers has the greatest number of distinct

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Bunuel
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Which of the following numbers has the greatest number of distinct [#permalink] New post   13 Apr 2016, 06:12
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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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D
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Re: Which of the following numbers has the greatest number of distinct [#permalink] New post   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
Answer D
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ameyaprabhu
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Re: Which of the following numbers has the greatest number of distinct [#permalink] New post   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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Bunuel
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Re: Which of the following numbers has the greatest number of distinct [#permalink] New post   14 May 2017, 05:34
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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] New post   18 May 2017, 20:01
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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.

Answer: D
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Re: Which of the following numbers has the greatest number of distinct [#permalink] New post   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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BrentGMATPrepNow
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Re: Which of the following numbers has the greatest number of distinct [#permalink] New post   05 Mar 2020, 07:16
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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


This requires us to find the prime factorization of each answer choice

A. 165 = (3)(5)(11) --- 3 distinct prime factors
B. 192 = (2)(2)(2)(2)(2)(2)(3) --- 2 distinct prime factors
C. 228 = (2)(2)(3)(19) --- 3 distinct prime factors
D. 330 = (2)(3)(5)(11) --- 4 distinct prime factors
E. 332 = (2)(2)(83) --- 2 distinct prime factors

Answer: D

Cheers,
Brent
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Re: Which of the following numbers has the greatest number of distinct [#permalink] New post   20 Apr 2024, 03:22
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