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# Find the maximum value of n such that 77!

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Retired Moderator
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
Find the maximum value of n such that 77!  [#permalink]

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02 Mar 2017, 04:08
1
00:00

Difficulty:

(N/A)

Question Stats:

60% (02:40) correct 40% (01:34) wrong based on 5 sessions

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Find the maximum value of n such that 77! is perfectly divisible by 720^n.

(A) 35
(B) 18
(C) 17
(D) 36
(E) 38

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Intern
Joined: 28 Jul 2011
Posts: 30
Location: United Kingdom
WE: Corporate Finance (Energy and Utilities)
Re: Find the maximum value of n such that 77!  [#permalink]

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02 Mar 2017, 04:23
We need to find the power of 720.
What is 720 made up of : 2X2X2X2X3X3X5

now we will have plenty of 2s and 3s in the 77! - so we just have to count the number of 5s appearing in the 77!
for this you can use the formula = 77/5 + 77/25 = 15 + 2 = 17

So we will have 17 5s in the 77! so 17 720s
Intern
Joined: 05 Oct 2016
Posts: 4
Re: Find the maximum value of n such that 77!  [#permalink]

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02 Mar 2017, 06:30
Is there another way to solve this?

--== 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: Find the maximum value of n such that 77! &nbs [#permalink] 02 Mar 2017, 06:30
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