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# What is the remainder of 13^81 when divided by 10?

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Intern
Joined: 27 Jan 2018
Posts: 1
What is the remainder of 13^81 when divided by 10?  [#permalink]

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09 Mar 2018, 02:37

Sent from my iPad using GMAT Club Forum mobile app

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

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BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 874
Location: India
GMAT 1: 710 Q49 V36
Re: What is the remainder of 13^81 when divided by 10?  [#permalink]

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09 Mar 2018, 02:39
13^81 mod 10

13 mod 10 = 3

13^2 mod 10 = 9

13^3 mod 10 = 7

13^4 mod 10 = 1

13^5 mod 10 = 3

so we can a cycle of 4

3,9,7,1 for last digit

and thus 81 = 4k+1

so 13 mod 10 and 13^81 mod 10 will have same last digit

1
Math Expert
Joined: 02 Sep 2009
Posts: 52363
Re: What is the remainder of 13^81 when divided by 10?  [#permalink]

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12 Mar 2018, 07:45
leeminhanh wrote:

Sent from my iPad using GMAT Club Forum mobile app

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. 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: What is the remainder of 13^81 when divided by 10? &nbs [#permalink] 12 Mar 2018, 07:45
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