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If N is a positive integer what is the remainder when 2^N

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If N is a positive integer what is the remainder when 2^N [#permalink]

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If N is a positive interger what is the remainder when \(2^N\) is divided by 10?

1. N is divisible by 2
2. N is divisible by 4
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Re: If N is a positive integer what is the remainder when 2^N [#permalink]

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New post 18 Oct 2016, 00:46
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gaurav_raos wrote:
If N is a positive interger what is the remainder when \(2^N\) is divided by 10?

1. N is divisible by 2
2. N is divisible by 4


any integer divided by 10 , the remainder is the last digit , so question asks what is the last digit for 2^n. but 2^n has a pattern when it comes to its last digit , a cycle where the last digit repeats

2^1 = 2 , 2^2 = 4 , 2^3 = 8 , 2^4 = 16 , 2^5 =32 , 2^6 = 64, ( if you look at the pattern last digit is (2,4,8,6,2,4,8,6....)

from 1

N is even , thus 2^n could end in either 4 or 6 .... insuff

from 2
N is Divisible by 4 ie 2^n = 2^4m , thus 2^4m will always ends in 6 .... suff and the last digit when 2^4m/10 is 6

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Re: If N is a positive integer what is the remainder when 2^N [#permalink]

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New post 13 Jun 2017, 03:37
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I have a doubt here in selection of B as an answer.
What if it is 2^4*0 it would be 2^0= 1 and the remainder would not be 6
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Re: If N is a positive integer what is the remainder when 2^N [#permalink]

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New post 13 Jun 2017, 05:49
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If N is a positive integer what is the remainder when 2^N [#permalink]

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New post 06 Apr 2018, 08:12
shikha.lakhani wrote:
I have a doubt here in selection of B as an answer.
What if it is 2^4*0 it would be 2^0= 1 and the remainder would not be 6


Missed to note this, if like Bunuel pointed out Positive integer wasnt mentioned i would have gotten this question wrong .. Kudos to you for thinking it..
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If N is a positive integer what is the remainder when 2^N   [#permalink] 06 Apr 2018, 08:12
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