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Re: What is the remainder when 3^7 is divided by 8? [#permalink]
1
\(3^7=3*9^3\)
for odd power of 9, the unit's digit is 9
for even power of 9, the unit's digit is 1

here, power of 3 is odd and 3*1/8 results in remainder of 3. Answer is C
Carcass wrote:
What is the remainder when \(3^7\) is divided by 8?

(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
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Re: What is the remainder when 3^7 is divided by 8? [#permalink]
We need to find What is the remainder when \(3^7\) is divided by 8

Theory: Remainder of a * b by a number say 8 is same as remainder of a by 8 * remainder of b by 8

\(3^7\) = \(3^(2 + 2 + 2 + 1)\) = \(3^2 * 3^2 * 3^2 * 3^1\) = 3 * \(3^2 * 3^2 * 3^2\)

=> Remainder of \(3^7\) by 8 is same as Remainder of 3 by 8 * Remainder of \(3^2\) by 8 * Remainder of \(3^2\) by 8 * Remainder of \(3^2\) by 8

= 3 * 1 * 1 * 1 = 3

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: What is the remainder when 3^7 is divided by 8? [#permalink]
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Re: What is the remainder when 3^7 is divided by 8? [#permalink]
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