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

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What is the remainder when 3^283 is divided by 5? [#permalink] New post 17 Dec 2017, 14:12
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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
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Re: What is the remainder when 3^283 is divided by 5? [#permalink] New post 18 Dec 2017, 02:11
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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?
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Re: What is the remainder when 3^283 is divided by 5? [#permalink] New post 18 Dec 2017, 11:55
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No. The only way is the pattern, that is the fastest approach, by the way.

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

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