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Find the remainder when 51^203 is divided by 7

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Find the remainder when 51^203 is divided by 7 [#permalink]

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New post 26 Jan 2017, 19:23
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Question Stats:

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Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5

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Find the remainder when 51^203 is divided by 7 [#permalink]

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New post 26 Jan 2017, 19:31
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saswata4s wrote:
Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5


Hi,
\(51^{203}=(49+2)^{203}\)
Here all terms except 2^203 will be div by 7..

Now \(2^{203}=(2^3)^{67}*2^2=8^{67}*4=(7+1)^{67}*4\)
Here \((7+1)^{67}\) will leave a remainder of 1, so remainder=1*4=4

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Re: Find the remainder when 51^203 is divided by 7 [#permalink]

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New post 27 Jan 2017, 03:40
saswata4s wrote:
Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5



A is the answer..51 will give 2 as remainder ..(
So 2^203/7
(2^3)^67 * 4/7
(8^67 * 4)/7 (if a equation in form (ax+1)/x then the remainder will be 1(here (7*1+1)/7)
8^67 will give remainder =1
1*4/7=4 is the remainder
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Re: Find the remainder when 51^203 is divided by 7 [#permalink]

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New post 27 Jan 2017, 03:53
Thank you @chatun2u for the explanation. Although I got the answer correct, i wasn't sure about it.
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Re: Find the remainder when 51^203 is divided by 7 [#permalink]

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New post 11 Mar 2018, 00:33
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Re: Find the remainder when 51^203 is divided by 7   [#permalink] 11 Mar 2018, 00:33
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Find the remainder when 51^203 is divided by 7

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