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

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Senior Manager
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What is the smallest non-prime positive integer that is not a factor  [#permalink]

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Updated on: 09 Aug 2019, 22:20
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Question Stats:

70% (01:15) correct 30% (01:23) wrong based on 50 sessions

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What is the smallest non-prime positive integer that is not a factor of 5040 ?

A) 7
B) 8
C) 11
D) 12
E) 22

Originally posted by fauji on 09 Aug 2019, 21:18.
Last edited by Bunuel on 09 Aug 2019, 22:20, edited 1 time in total.
Renamed the topic.
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Re: What is the smallest non-prime positive integer that is not a factor  [#permalink]

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09 Aug 2019, 21:28
(E) just divide the non-prime by checking divisibility checks. No need to find factors. You can save time in such questions.
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Re: What is the smallest non-prime positive integer that is not a factor  [#permalink]

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10 Aug 2019, 02:25
Options A&c are prime numbers.✖
Options B&D are the factors of the number✖
so Option E would be the answer.

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

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13 Aug 2019, 06:25
Explanation:

To find: The smallest non-prime positive integer that is not a factor of 5040

We can solve this question in 2 ways:

- 5040 is actually 7!
Hence we need to find the smallest NON-prime positive integer that is NOT a factor of 7!(5040)

After 7 we have 11 as next positive prime number. To make it non-prime we need to multiply with 2
So 11 * 2 = 22 Answer => option E

- Another approach is to negate and check options:
option A & C straightaway eliminated for being prime values.
Among options B,D, and E - check manually => Final Answer we get is option E
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Re: What is the smallest non-prime positive integer that is not a factor  [#permalink]

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13 Aug 2019, 06:26
Similar Practice question:

https://gmatclub.com/forum/what-is-the- ... l#p2336113
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Re: What is the smallest non-prime positive integer that is not a factor  [#permalink]

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14 Aug 2019, 01:06
fauji wrote:
What is the smallest non-prime positive integer that is not a factor of 5040 ?

A) 7
B) 8
C) 11
D) 12
E) 22

As soon as i saw the question i picked up my pen and started using divisibility rules starting from 3 and went upto 12.
When i finally looked up, i saw the answers and cursed myself, ALOT!
7,11 are primes, hence out of the question.
All you need to check is div by 4, 3 & 8, which will hardly take 15 sec and you'll have your answer!

DON'T BE AN OSTRICH, BE SMART!
Re: What is the smallest non-prime positive integer that is not a factor   [#permalink] 14 Aug 2019, 01:06