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What is the least positive integer that is not a factor of a

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What is the least positive integer that is not a factor of a [#permalink] New post 19 Jan 2016, 15:16
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Question Stats:

71% (01:04) correct 28% (00:45) wrong based on 77 sessions
What is the least positive integer that is not a factor of 25! and is not a prime number?

A 26
B 28
C 36
D 56
E 58

Practice Questions
Question: 21
Page: 343
Difficulty: hard
[Reveal] Spoiler: OA

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Last edited by Carcass on 15 Dec 2018, 15:49, edited 2 times in total.
Edited by Carcass
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Re: What is the least positive integer that is not a factor of a [#permalink] New post 19 Jan 2016, 15:37
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Solution

This question is really tricky. It could be daunting if you do not use the right strategy

What we do know is that 25 factorial \(25!\) is equal to \(25*24*23*22.........*1\) inclusive. Now every number that is in between this range is a factor of \(25!\) and every number outside this range but is the result of a multiplication of two numbers of the range, then is also a factor of \(25!.\)

To give an example: choice A is 26 and this is \(2*13\); these two numbers are both factors of \(25!.\) Looking at the answer choices, we do notice that choice E 58 is the result of \(2*29\).

2 is a factor of \(25 !\) but 29 it is not.

Be careful reading the question: all the answer choice but E are prime factors or simply factors in between the range. E has a prime in but 29 is out. So is the only possible answer

The answer is \(E\)
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Re: What is the least positive integer that is not a factor of a [#permalink] New post 15 Dec 2018, 13:51
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Carcass wrote:
What is the least positive integer that is not a factor of and is not a 25! prime number?

 A 26
 B 28
 C 36
 D 56
 E 58

Practice Questions
Question: 21
Page: 343
Difficulty: hard


I don't understand the wording of the problem. It says "not a factor of and not a 25! prime number", is it me or is that really poor grammar?
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Re: What is the least positive integer that is not a factor of a [#permalink] New post 15 Dec 2018, 15:50
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The 25! was in the wrong place in the stem.

Now is fixed.

Thank you so much :)

Regards
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Re: What is the least positive integer that is not a factor of a [#permalink] New post 09 May 2020, 02:06
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25! = 25*24*23*...*3*2*1

Answer choices:

26=2*13
28=2*2*7
36=2*2*3*3
56=2*2*2*7
58=2*29

58 is the only number that is not a prime and also not a factor of 25!
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Re: What is the least positive integer that is not a factor of a   [#permalink] 09 May 2020, 02:06
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