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Intern  B
Joined: 17 Aug 2019
Posts: 20
Re: The remainder when ((6^6)^6)^6… is divided by 10 is  [#permalink]

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The unit digit of 6 to the power of any finite positive integer will always be 6. Therefore, the remainder would be 6.
Intern  B
Joined: 13 Aug 2013
Posts: 22
Location: India
Concentration: Technology, General Management
Re: The remainder when ((6^6)^6)^6… is divided by 10 is  [#permalink]

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For any integer n > 0, last digit of 6^n is 6.
Thus, remainder will be 6 when divided by 10.
Intern  B
Joined: 14 Oct 2019
Posts: 1
Re: The remainder when ((6^6)^6)^6… is divided by 10 is  [#permalink]

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when 6 is divided by 10, remainder is 6
now, 6^n where n is a natural no, last digit is always 6. this is a unique characteristics of 6.

last digit means the remainder when divided by 10.
so 6 to the power anything will give rem 6 when divided by 10.
Intern  B
Joined: 30 Jun 2016
Posts: 14
Re: The remainder when ((6^6)^6)^6… is divided by 10 is  [#permalink]

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The last digit of anything to the power of 6 always yields 6 in the last digit. So remainder here would be 6.

Posted from my mobile device Re: The remainder when ((6^6)^6)^6… is divided by 10 is   [#permalink] 06 Jan 2020, 01:21

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# The remainder when ((6^6)^6)^6… is divided by 10 is  