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# What is the remainder when 3^283 is divided by 5?

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Moderator
Joined: 18 Apr 2015
Posts: 5185
Followers: 77

Kudos [?]: 1040 [0], given: 4676

What is the remainder when 3^283 is divided by 5? [#permalink]  17 Dec 2017, 14:12
Expert's post
00:00

Question Stats:

100% (00:33) correct 0% (00:00) wrong based on 3 sessions
What is the remainder when $$3^{283}$$ is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4
_________________
Manager
Joined: 25 Nov 2017
Posts: 51
Followers: 0

Kudos [?]: 41 [1] , given: 5

Re: What is the remainder when 3^283 is divided by 5? [#permalink]  18 Dec 2017, 02:11
1
KUDOS
For this question, we must know the pattern of 3.
3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = .... 3
So we have a pattern of 4.
When we divide 383 by 4 we got 70,75. So the 280th ending must be a one. Then 283th must be a 7.
(Something ending with 7 / 5 = Quotient wth a remainder of 2.
So C.

Anyone has any other shortcuts for this one?
Moderator
Joined: 18 Apr 2015
Posts: 5185
Followers: 77

Kudos [?]: 1040 [0], given: 4676

Re: What is the remainder when 3^283 is divided by 5? [#permalink]  18 Dec 2017, 11:55
Expert's post
No. The only way is the pattern, that is the fastest approach, by the way.

Regards
_________________
Re: What is the remainder when 3^283 is divided by 5?   [#permalink] 18 Dec 2017, 11:55
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