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

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Manager
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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17 Aug 2016, 12:06
7
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:26) correct 48% (01:16) wrong based on 129 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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Senior Manager
Joined: 23 Apr 2015
Posts: 302
Location: United States
WE: Engineering (Consulting)
Re: What is the greatest value of n such that 18n is a factor of 18! ?  [#permalink]

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17 Aug 2016, 12:15
1
1
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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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.

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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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30 Aug 2016, 17:42
1
Here is what i would do =>
Number of 3's=> 18/3+18/9=> hence there are 8 3's . So number of 9's = 4
clearly there are more than 4 2's
Thus number of 18 => 4
SMASH that 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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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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