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# What is the greatest value of x such that 8^x is a factor of

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VP
Joined: 21 Jul 2006
Posts: 1491
What is the greatest value of x such that 8^x is a factor of [#permalink]

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17 Oct 2008, 07:27
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1. What is the greatest value of $$x$$ such that $$8^x$$ is a factor of 16!?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

2. What is the greatest value of q such that 9^q is a factor of 21! ?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6

Please show me the fastest way to approach this.

Thanks

--== Message from GMAT Club Team ==--

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Last edited by tarek99 on 23 Oct 2008, 09:30, edited 1 time in total.
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown
Re: PS: greatest value of x [#permalink]

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17 Oct 2008, 13:05
C = 5

This is how approached it

8^x = 2^(3x)
From 16! pick all the number that can be divided by 2

16*8*4*2 = 2^10
and
14*12*10*6 = 2^5

so 2^(3x) = 2^15
x=5

I am sure there are formulae to solve it more easily, but this is what I could do
Manager
Joined: 04 Sep 2008
Posts: 239
Location: Kolkata
Schools: La Martiniere for Boys
Re: PS: greatest value of x [#permalink]

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21 Oct 2008, 06:02
Here's a better approach...

Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.

Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.

Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1

therefore 5
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Thanks
rampuria

VP
Joined: 30 Jun 2008
Posts: 1019
Re: PS: greatest value of x [#permalink]

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22 Oct 2008, 02:38
rampuria wrote:
Here's a better approach...

Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.

Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.

Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1

therefore 5

Agreed
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"You have to find it. No one else can find it for you." - Bjorn Borg

VP
Joined: 05 Jul 2008
Posts: 1373
Re: PS: greatest value of x [#permalink]

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22 Oct 2008, 09:32
My approach was to figure out how many 8's I can make out of 16!

16 = 8 X 2 14 = 2 X 7 and so on for all even numbers.

8 can also be arrived at by 2 ^ 3 or 4 X 2 ( such numbers are formed from left out of numbers of 14 , 12 etc)

we get 5 eights and hence x=5
VP
Joined: 21 Jul 2006
Posts: 1491
Re: PS: greatest value of x [#permalink]

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22 Oct 2008, 16:48
rampuria wrote:
Here's a better approach...

Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.

Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.

Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1

therefore 5

so according to your approach, how would you then solve this problem:

What is the greatest value of $$q$$ such that $$9^q$$ is a factor of 21! ?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Intern
Joined: 03 Mar 2008
Posts: 44
Re: PS: greatest value of x [#permalink]

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22 Oct 2008, 19:28
LiveStronger wrote:
C - 4

3^8 = 3^2q
q = 4

for whatever reason i m getting 3^9 = 3^2q
Pls help me see why ?

3 6 9 12 15 18 21 = 3^9
1+1+2+1+1+2+1=9

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: PS: greatest value of x   [#permalink] 22 Oct 2008, 19:28
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