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What is the remainder when 3^7 is divided by 8?

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Posts: 59725
What is the remainder when 3^7 is divided by 8?  [#permalink]

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04 Apr 2019, 00:31
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Difficulty:

35% (medium)

Question Stats:

63% (01:06) correct 37% (00:51) wrong based on 99 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

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

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04 Apr 2019, 00:35
$$\frac{3^7}{8}$$

= $$\frac{(3^2)^3 *3}{8}$$

= $$\frac{(9)^3 * 3}{8}$$

9 divided by 8 will always leave a remainder 1

= $$\frac{(1)^3 * 3}{8}$$

= $$\frac{3}{8}$$

Remainder = 3

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

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04 Apr 2019, 00:53

Solution

To find:
• Remainder when $$3^7$$ is divided by 8

Approach and Working:
• $$3^7$$ = $$3^6$$ × 3 = $$(3^2)^3$$ × 3 = $$9^3$$ × 3

Remainder when $$9^3$$ × 3 is divided by 8:
• $$(\frac{9^3 × 3}{8})$$R = $$(\frac{1^3 × 3}{8})$$R = 3

Hence, the correct answer is option C.

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

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04 Apr 2019, 03:29
Bunuel wrote:
What is the remainder when 3^7 is divided by 8?

(A) 1
(B) 2
(C) 3
(D) 5
(E) 7

3^7 = 9*3^5
3^5 = cyclicity we get 3
and 9 divided by 8 gives remainder 1
1*3 = 3
IMO C
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Re: What is the remainder when 3^7 is divided by 8?  [#permalink]

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07 Apr 2019, 19:08
1
Bunuel wrote:
What is the remainder when 3^7 is divided by 8?

(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.

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

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07 Apr 2019, 20:29
I did it in pure cyclist, 3^7 gives unit value of 7, and when 7/8 gives 7 as remainder? can any expert please tell me where I went wrong?
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Re: What is the remainder when 3^7 is divided by 8?  [#permalink]

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07 Apr 2019, 20:40
Shef08 wrote:
I did it in pure cyclist, 3^7 gives unit value of 7, and when 7/8 gives 7 as remainder? can any expert please tell me where I went wrong?

Just units digit may not give you the remainder. For example, will you get the same remainder everytime when 7, 17, 27, 37 etc are divided by 8?

So, in case you are trying to determine the remainder by 7, just considering the units digit of the number is not the correct approach.
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Re: What is the remainder when 3^7 is divided by 8?   [#permalink] 07 Apr 2019, 20:40
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