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What is the remainder when 2^28 is divided by 3?

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Bunuel
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What is the remainder when 2^28 is divided by 3? [#permalink] New post   06 Dec 2016, 07:35
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What is the remainder when 2^28 is divided by 3?

A. 1
B. 2
C. 3
D. 4
E. 5
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A
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Abhishek009
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Re: What is the remainder when 2^28 is divided by 3? [#permalink] New post   06 Dec 2016, 07:51
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Bunuel wrote:
What is the remainder when 2^28 is divided by 3?

A. 1
B. 2
C. 3
D. 4
E. 5


\(2^{28} = 16^{7}\)

Remainer of \(\frac{16}{3} = 1\)

So, remainder of \(2^{28} = 1\) ; Answer will be (A) 1
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Re: What is the remainder when 2^28 is divided by 3? [#permalink] New post   08 Dec 2016, 11:40
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Option A)

Remainder \(\frac{2^{28}}{3}\) = Remainder \(\frac{((3 - 1) ^ {28})}{3}\) = Remainder \(\frac{(-1)^{28}}{3}\) = Remainder \(\frac{1}{3}\) = 1
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Re: What is the remainder when 2^28 is divided by 3? [#permalink] New post   19 Nov 2018, 19:29
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I used a different method than those mentioned above, but came out with the same answer.

In this particular question, there was a pattern to the remainders:
(2^1)/3 = 0 (with a remainder of 2)
(2^2)/3 = 1 (with a remainder of 1)
(2^3)/3 = 2 (with a remainder of 2)
(2^4)/3 = 5 (with a remainder of 1)

...and the pattern continues where the odd powers have remainders = 2 and the even powers have remainders = 1.

Using the above, because 28 is an even power, the remainder will be 1.
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Re: What is the remainder when 2^28 is divided by 3? [#permalink] New post   06 Nov 2019, 20:27
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Bunuel wrote:
What is the remainder when 2^28 is divided by 3?

A. 1
B. 2
C. 3
D. 4
E. 5


Let’s determine the pattern of remainders when a base of 2 is divided by 3.

2^1 / 3 = 0 remainder 2

2^2 / 3 = 1 remainder 1

2^3 / 3 = 2 remainder 2

2^4 / 3 = 5 remainder 1

We see that when 2 is raised to an even power and divided by 3, the remainder is 1. Thus, the remainder when 2^28 is divided by 3 is 1.

Answer: A
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What is the remainder when 2^28 is divided by 3? [#permalink] New post   13 Dec 2019, 01:53
why is the answer from the usual 2^28 not resulting in the answer.

2^28 = 2^4k = which is 6, so 6/3 remainder is 0

:( what is wrong in the approach ? ( i also understand that 0 isn't in the choices. But I'd like to know why this method isn't right )
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What is the remainder when 2^28 is divided by 3? [#permalink]
13 Dec 2019, 01:53
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