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What is the greatest value of n such that 18n is a factor of 18! ?

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What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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New post 17 Aug 2016, 12:06
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A
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Question Stats:

52% (01:26) correct 48% (01:15) wrong based on 128 sessions

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What is the greatest value of n such that 18^n is a factor of 18! ?

A) 1
B) 2
C) 3
D) 4
E) 5

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Re: What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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New post 17 Aug 2016, 12:15
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duahsolo wrote:
What is the greatest value of n such that 18^n is a factor of 18! ?

A) 1
B) 2
C) 3
D) 4
E) 5


Prime factoring 18 will give \((2*3*3) = (2*3^2)\)

The numbers that has of 3's in 18! are 3(one 3), 6(one 3), 9(3*3, two 3's), 12(one 3), 15(one 3), 18(two 3's) and total Eight 3's

So the max value for n in \(18^n\) equal to 4.



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Re: What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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New post 20 Aug 2016, 03:04
Another way to solve this question :

We know that 18 = 2 *3^2.

Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)

No. of 3s = 18/3 = 6/3 = 2.

Add the numbers in Bold, you will get total number of 3s = 8.

Hence, total number of 3^2 = 8/2 = 4.

Hence, answer is 4. D
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Re: What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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Re: What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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New post 25 Aug 2018, 08:53
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Re: What is the greatest value of n such that 18n is a factor of 18! ? &nbs [#permalink] 25 Aug 2018, 08:53
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