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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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GPA: 3.39
What is the remainder when 2^20 is divided by 10?
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14 Sep 2022, 06:58
14 Sep 2022, 06:58
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What is the remainder when 2^20 is divided by 10?
A. 0
B. 2
C. 4
D. 6
E. 8
A. 0
B. 2
C. 4
D. 6
E. 8
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: What is the remainder when 2^20 is divided by 10?
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16 Sep 2022, 08:23
16 Sep 2022, 08:23
1
What is the remainder of \(2^{20}\) when divided by 10
Theory: Remainder of a number by 10 is same as the unit's digit of the number
(Watch this Video to Learn How to find Remainders of Numbers by 10)
Using Above theory Remainder of \(2^{20}\) by 10 = unit's digit of \(2^{20}\)
Now to find the unit's digit of \(2^{20}\), we need to find the pattern / cycle of unit's digit of power of 2 and then generalizing it.
Unit's digit of \(2^1\) = 2
Unit's digit of \(2^2\) = 4
Unit's digit of \(2^3\) = 8
Unit's digit of \(2^4\) = 6
Unit's digit of \(2^5\) = 2
So, unit's digit of power of 2 repeats after every \(4^{th}\) number.
=> We need to divided 20 by 4 and check what is the remainder
=> 20 divided by 4 gives 0 remainder
=> \(2^{20}\) will have the same unit's digit as \(2^4\) = 6
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Remainder of a number by 10 is same as the unit's digit of the number
(Watch this Video to Learn How to find Remainders of Numbers by 10)
Using Above theory Remainder of \(2^{20}\) by 10 = unit's digit of \(2^{20}\)
Now to find the unit's digit of \(2^{20}\), we need to find the pattern / cycle of unit's digit of power of 2 and then generalizing it.
Unit's digit of \(2^1\) = 2
Unit's digit of \(2^2\) = 4
Unit's digit of \(2^3\) = 8
Unit's digit of \(2^4\) = 6
Unit's digit of \(2^5\) = 2
So, unit's digit of power of 2 repeats after every \(4^{th}\) number.
=> We need to divided 20 by 4 and check what is the remainder
=> 20 divided by 4 gives 0 remainder
=> \(2^{20}\) will have the same unit's digit as \(2^4\) = 6
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Remainders
gmatclubot
Re: What is the remainder when 2^20 is divided by 10? [#permalink]
16 Sep 2022, 08:23
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