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

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What is the highest power of 7 in 5000!? (5000! means [#permalink] New post 20 Oct 2003, 03:30
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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.
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Re: PS: Powers of 7 [#permalink] New post 20 Oct 2003, 10:56
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
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 [#permalink] New post 20 Oct 2003, 12:45
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, 06:41
Answer is: 832
Adhi's approach is right.
thanks
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 [#permalink] New post 30 Oct 2003, 14:33
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, 14:33
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