When 8101-8 is divided by 10, what is the remainder?

When \(8^{101}-8\) is divided by 10, what is the remainder

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 \(8^{101}-8\) by 10 unit's digit of \(8^{101}-8\)

Now, Let's find the unit's digit of \(8^{101}\) first.

We can do this by finding the pattern / cycle of unit's digit of power of 8 and then generalizing it.

Unit's digit of \(8^1\) = 8
Unit's digit of \(8^2\) = 4
Unit's digit of \(8^3\) = 2
Unit's digit of \(8^4\) = 6
Unit's digit of \(8^5\) = 8

So, unit's digit of power of 8 repeats after every \(4^{th}\) number.
=> We need to divided 101 by 4 and check what is the remainder
=> 101 divided by 4 gives 1 remainder

=> \(8^{101}\) will have the same unit's digit as \(8^1\) = 8
=> Unit's digits of \(8^{101}-8\) = 8 - 8 = 0

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Remainders

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