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Remainder when 25^10 is divided by 576?

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Remainder when 25^10 is divided by 576?  [#permalink]

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New post Updated on: 14 Oct 2018, 05:20
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Question Stats:

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Remainder when 25^10 is divided by 576?

1) 241
2) 542
3) 378
4) 405
5) None of these

Posted from my mobile device

Originally posted by asifahmed500 on 14 Oct 2018, 04:48.
Last edited by asifahmed500 on 14 Oct 2018, 05:20, edited 3 times in total.
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Re: Remainder when 25^10 is divided by 576?  [#permalink]

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New post 14 Oct 2018, 07:59
asifahmed500 wrote:
Remainder when 25^10 is divided by 576?

1) 241
2) 542
3) 378
4) 405
5) None of these

Posted from my mobile device


\(Rem(\frac{25^{10}}{576})\)=\(Rem(\frac{(24+1)^{10}}{24^2})\)

Upon expansion of \((24+1)^{10}\), the terms will have 24 raised to the power from 0 to 24. Out of which, the terms with \(24^0\) and \(24^1\) are not divisible by \(24^2\). OR the terms with 24 raised to the power greater than or equal to 2 are divisible by \(24^2\).

So, \(Rem(\frac{(24+1)^{10}}{24^2})\)=\(10C0*24^0+10C1*24^1=1+10*24=241\)

Ans. (A)
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Re: Remainder when 25^10 is divided by 576?  [#permalink]

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New post 14 Oct 2018, 08:06
asifahmed500 wrote:
Remainder when 25^10 is divided by 576?

1) 241
2) 542
3) 378
4) 405
5) None of these

Posted from my mobile device


OA: A

Remainder \(\frac{25^{10}}{576}\)=Remainder \(\frac{625^{5}}{576}\)=Remainder \(\frac{49^{5}}{576}\)=Remainder \(\frac{97*97*49}{576}\)=Remainder \(\frac{145*97}{576}\)=Remainder \(\frac{241}{576}\)

Remainder\(= 241\)
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Re: Remainder when 25^10 is divided by 576?   [#permalink] 14 Oct 2018, 08:06
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Remainder when 25^10 is divided by 576?

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