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# If 60! is written out as an integer, with how many consecuti

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Intern
Joined: 28 May 2010
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If 60! is written out as an integer, with how many consecuti [#permalink]  20 Jul 2010, 19:13
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Question Stats:

83% (01:24) correct 17% (01:11) wrong based on 95 sessions
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?

A. 6
B. 12
C. 14
D. 42
E. 56

Clearly there are 12 multiples of 5, therefore, 12 zeros. I don't understand....
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 05:32, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 49587 [0], given: 7395

Re: Hard tricky question [#permalink]  20 Jul 2010, 19:23
Expert's post
knabi wrote:
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
6
12
14
42
56

Clearly there are 12 multiples of 5, therefore, 12 zeros. I don't understand....

$$\frac{60}{5}+\frac{60}{5^2}=12+2=14$$.

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Re: Hard tricky question [#permalink]  20 Jul 2010, 19:25
this formula is very useful...
Manager
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Re: Hard tricky question [#permalink]  20 Jul 2010, 23:34
Bunuel, can you elaborate more on this formula..
I would have found the number of times 5 is repeated to get to the answer..
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Intern
Joined: 01 Apr 2010
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Re: Hard tricky question [#permalink]  21 Jul 2010, 00:52
Hi Bunuel,

The explanation on the link is great..Is there a similar explanation on remainders and power cycle concepts?

Thanks,
SS
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Joined: 02 Sep 2009
Posts: 29090
Followers: 4720

Kudos [?]: 49587 [0], given: 7395

Re: Hard tricky question [#permalink]  21 Jul 2010, 09:00
Expert's post
SS2010 wrote:
Hi Bunuel,

The explanation on the link is great..Is there a similar explanation on remainders and power cycle concepts?

Thanks,
SS

Check Math: Number Theory for powers and cycles: math-number-theory-88376.html

Check sriharimurthy's post on remainders: compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html

temp33 wrote:
Bunuel, can you elaborate more on this formula..
I would have found the number of times 5 is repeated to get to the answer..

Hope it helps.
_________________
Re: Hard tricky question   [#permalink] 21 Jul 2010, 09:00
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