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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
Posts: 31
If 60! is written out as an integer, with how many consecuti [#permalink]

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Updated on: 09 Jul 2013, 06:32
2
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Difficulty:

5% (low)

Question Stats:

82% (00:21) correct 18% (01:07) wrong based on 288 sessions

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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....

Originally posted by knabi on 20 Jul 2010, 20:13.
Last edited by Bunuel on 09 Jul 2013, 06:32, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 46305
Re: Hard tricky question [#permalink]

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20 Jul 2010, 20:23
1
4
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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Posts: 188
Re: Hard tricky question [#permalink]

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20 Jul 2010, 20:25
this formula is very useful...
Manager
Joined: 20 Jul 2010
Posts: 150
Re: Hard tricky question [#permalink]

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21 Jul 2010, 00:34
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
Posts: 10
Re: Hard tricky question [#permalink]

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21 Jul 2010, 01:52
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: 46305
Re: Hard tricky question [#permalink]

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21 Jul 2010, 10:00
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..

Formula explained here: everything-about-factorials-on-the-gmat-85592.html?hilit=trailing#p669230

Hope it helps.
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Re: If 60! is written out as an integer, with how many consecuti [#permalink]

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28 Feb 2017, 10:29
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Re: If 60! is written out as an integer, with how many consecuti   [#permalink] 28 Feb 2017, 10:29
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# If 60! is written out as an integer, with how many consecuti

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