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Bunuel
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What is the remainder when 2^26 is divided by 6 ? 21 Jul 2022, 03:07
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D
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63% (00:59) correct 37% (01:25) wrong based on 226 sessions

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What is the remainder when 2^26 is divided by 6 ?

A. 0
B. 2
C. 3
D. 4
E. 5
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D
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What is the remainder when 2^26 is divided by 6 ? 21 Jul 2022, 03:24
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What is the remainder when 2^26 is divided by 6 ?

A. 0
B. 2
C. 3
D. 4
E. 5
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remainder when 2^1 is divided by 6 is 2
remainder when 2^2 is divided by 6 is 4
remainder when 2^3 is divided by 6 is 2
remainder when 2^4 is divided by 6 is 4

as can be seen whenever 2 has even power remainder is 4. Thus answer should be 4.
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What is the remainder when 2^26 is divided by 6 ? 21 Jul 2022, 12:04
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The cyclicity of 2 is 4. so ultimately it will be 2^2/6, which will give the remainder of 4 (Option D)
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What is the remainder when 2^26 is divided by 6 ? 05 Aug 2022, 09:32
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Hello! Could we also use the binomial theorem?
In this case I obtain 2^25 / 3 = [2 * (2^2)^12 ]/3 = [2 * (3+1)^12 ]/3 with remainder 2

Can you help me please?
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What is the remainder when 2^26 is divided by 6 ? Updated on: 18 Sep 2024, 09:17
Originally posted by BrushMyQuant on 18 Sep 2024, 08:21.
Last edited by BrushMyQuant on 18 Sep 2024, 09:17, edited 1 time in total.
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We need to find the remainder when \(2^{26}\) is divided by 6?

To solve this problem we need to find the cycle of remainder of power of 2 when divided by 6

Remainder of \(2^1\) (=2) by 6 = 2
Remainder of \(2^2\) (=4) by 6 = 4
Remainder of \(2^3\) (=8) by 6 = 2
Remainder of \(2^4\) (=16) by 6 = 4

=> Cycle is 2

=> Odd Power remainder is 2
=> Even power remainder is 4
=> Remainder of \(2^{26}\) is divided by 6 = 4

So, Answer will be D
Hope it Helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

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What is the remainder when 2^26 is divided by 6 ? 18 Sep 2024, 08:23
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DaniPare
Hello! Could we also use the binomial theorem?
In this case I obtain 2^25 / 3 = [2 * (2^2)^12 ]/3 = [2 * (3+1)^12 ]/3 with remainder 2

Can you help me please?
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While finding remainders you cannot cancel the common multiples
i.e. Remainder of 4/6 which is 4 is not same as remainder of 2/3 which is 2

So, 2^26 divided by 6 cannot be reduced to 2^25 divided by 3 for remainders
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