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Sub 505 Level|   Remainders|      
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AndreV
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The remainder when ((6^6)^6)^6… is divided by 10 is 05 Jan 2020, 13:24
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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.
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The remainder when ((6^6)^6)^6… is divided by 10 is 05 Jan 2020, 13:34
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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.
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The remainder when ((6^6)^6)^6… is divided by 10 is 05 Jan 2020, 14:04
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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.
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The remainder when ((6^6)^6)^6… is divided by 10 is 06 Jan 2020, 02:21
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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.

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The remainder when ((6^6)^6)^6… is divided by 10 is 06 Oct 2024, 06:04
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The remainder when ((6^6)^6)^6... is divided by 10 is

Problem is based on following two concepts:
  1. Remainder of a number by 10 = Units' digit of that number
  2. Units' digit of any positive integer power of 6 is 6

Units' digit of \(6^1\) = 6
Units' digit of \(6^2\) (=36) = 6
Units' digit of \(6^3\) (=216) = 6
.
.
.

So, units digit of ((6^6)^6)^6 = 6
=> Remainder of ((6^6)^6)^6 by 10 = Units' digit of ((6^6)^6)^6 = 6

So, Answer will be E
Hope it helps!


Link to Theory for Last Two digits of exponents here.

Link to Theory for Units' digit of exponents here.
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