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# Let n = 11!. What is the smallest non-prime positive intege

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Let n = 11!. What is the smallest non-prime positive intege [#permalink]  07 Aug 2017, 12:26
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Let n = 11!. What is the smallest non-prime positive integer that is not a factor of n?

[Reveal] Spoiler: OA
26

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Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]  30 Sep 2017, 06:09
To find the smallest non-prime number that is not a factor of k!, we have to take the first prime number greater than k and multiply it by 2 (at least for k greater than 6)
In our case, the smallest prime number greater than 11 is 13, that multiplied by 2 becomes 26.

More generally, the idea is to find the smallest number that cannot be computed as the product of any set of numbers composing 11!. With the rule above, the procedure of checking every number from 12 on is made faster
Re: Let n = 11!. What is the smallest non-prime positive intege   [#permalink] 30 Sep 2017, 06:09
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