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What is the remainder when 3^7 is divided by 8?
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14 Apr 2018, 02:47
14 Apr 2018, 02:47
Expert Reply
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Question Stats:
59% (01:01) correct
40% (00:39) wrong based on 102 sessions
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What is the remainder when \(3^7\) is divided by 8?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Re: What is the remainder when 3^7 is divided by 8?
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16 Apr 2018, 02:23
16 Apr 2018, 02:23
4
Take out some values of \(3\) when raised to the power
\(3^1 = 3\) when divided by \(8\) remainder \(= 3\)
\(3^2 = 9\) when divided by \(8\) remainder \(= 1\)
\(3^3 = 27\) when divided by \(8\) remainder \(= 3\)
\(3^4 = 81\) when divided by \(8\) remainder \(= 1\)
There is a continuous pattern of \(3\) and \(1\) repeating when \(3\) is raised to a power of something and is divided by\(8\)
Hence the possible ans choices are \(3\) and \(1\) however, \(3\) is the ans when \(3\) is raised to odd powers and \(1\) is the ans when \(3\) is raised to even power
therefore, option c
\(3^1 = 3\) when divided by \(8\) remainder \(= 3\)
\(3^2 = 9\) when divided by \(8\) remainder \(= 1\)
\(3^3 = 27\) when divided by \(8\) remainder \(= 3\)
\(3^4 = 81\) when divided by \(8\) remainder \(= 1\)
There is a continuous pattern of \(3\) and \(1\) repeating when \(3\) is raised to a power of something and is divided by\(8\)
Hence the possible ans choices are \(3\) and \(1\) however, \(3\) is the ans when \(3\) is raised to odd powers and \(1\) is the ans when \(3\) is raised to even power
therefore, option c
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Re: What is the remainder when 3^7 is divided by 8?
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07 Apr 2019, 17:44
07 Apr 2019, 17:44
1
Expert Reply
Carcass wrote:
What is the remainder when \(3^7\) is divided by 8?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
3^1/8 has a remainder of 3.
3^2/8 has a remainder of 1.
3^3/8 has a remainder of 3.
3^4/8 has a remainder of 1.
We see that when 3 raised to an odd power is divided by 8, the remainder is 3.
Answer: C
