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What is the highest power of 7 in 5000!? (5000! means

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Senior Manager
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What is the highest power of 7 in 5000!? (5000! means [#permalink] New post 20 Oct 2003, 02:30
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0% (00:00) correct 100% (01:58) wrong based on 1 sessions
What is the highest power of 7 in 5000!? (5000! means factorial 5000) (1) 4998 (2) 714 (3) 832 (4) 816

U have full 2 minutes.
GMAT Instructor
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Re: PS: Powers of 7 [#permalink] New post 20 Oct 2003, 09:56
Vicky wrote:
What is the highest power of 7 in 5000!? (5000! means factorial 5000) (1) 4998 (2) 714 (3) 832 (4) 816

U have full 2 minutes.


Hint: if you know what you are doing, you can solve this rather quickly!
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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 [#permalink] New post 20 Oct 2003, 11:45
Ans is C.832

Soln:

no of 7s in 5000! = 5000/7 + 5000/7^2 + 5000/7^3 +5000/7^4
= 714 + 102 + 14 + 2
so, highest power of 7 = 832
(we can not go beyond 7^4 since it is > 5000)
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 [#permalink] New post 25 Oct 2003, 05:41
Answer is: 832
Adhi's approach is right.
thanks
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 [#permalink] New post 30 Oct 2003, 13:33
Adhi wrote:
Ans is C.832

Soln:

no of 7s in 5000! = 5000/7 + 5000/7^2 + 5000/7^3 +5000/7^4
= 714 + 102 + 14 + 2
so, highest power of 7 = 832
(we can not go beyond 7^4 since it is > 5000)


Adhi, can you please explain how you came up with this, i don't get it.

Thanks
  [#permalink] 30 Oct 2003, 13:33
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