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

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Senior Manager
Joined: 21 Aug 2003
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What is the highest power of 7 in 5000!? (5000! means [#permalink]  20 Oct 2003, 02:30
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Question Stats:

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
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Re: PS: Powers of 7 [#permalink]  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

Intern
Joined: 13 Oct 2003
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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)
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
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Kudos [?]: 4 [0], given: 0

thanks
Intern
Joined: 17 Aug 2003
Posts: 38
Location: USA
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Kudos [?]: 1 [0], given: 0

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
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