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What is the smallest non-prime positive integer that is not a factor o

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New post 09 Aug 2019, 22:01
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (00:51) correct 33% (00:45) wrong based on 30 sessions

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What is the smallest non-prime positive integer that is not a factor of 12! ?

A) 12
B) 13
C) 14
D) 20
E) 26
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New post 09 Aug 2019, 22:13
After 12 there is 13 which is prime number✖
Then 14, 2×7 which there is in 12!✖
20,2×10, is also in 12!✖
Just 26 which is not the factor of 12!✔
Option E

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New post 09 Aug 2019, 22:32
E. 13 is not a factor of 12!. So 26 will also not a factor
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New post 11 Aug 2019, 00:34
Use the options.
E is correct.

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Re: What is the smallest non-prime positive integer that is not a factor o  [#permalink]

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New post 12 Aug 2019, 12:51
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Explanation:

To find: the smallest NON-prime positive integer that is NOT a factor of 12!

Since all the number before 12 would be divisible by 12!,

on further checking, next number:
13 (Prime- Not Applicable)
14 (Non-Prime but divisible by 12!)

We'll notice the list will go on till 25 (5*5) - time consuming approach.

Best approach:
Our nearest prime number is 13, to make it non-prime, we should multiply with 2 making it non-prime.
So 13*2 = 26 which becomes our answer.
Option E
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Re: What is the smallest non-prime positive integer that is not a factor o   [#permalink] 12 Aug 2019, 12:51
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