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Algebra

Hot goIITian

Joined:	14 Aug 2009
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26 Aug 2009 22:59:30 IST

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wats the remainder when 1!+2!+3!+...+175! is divided by 15?rates assured.

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wats the remainder when 1!+2!+3!+...+175! is divided by 15?rates assured.

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Baban

Blazing goIITian

Joined: 19 Oct 2007

Posts: 362

26 Aug 2009 23:09:05 IST

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See,15 divides all numbers from 15! tp 175!(since all the numbers conatain the factors 5 and 3).Therefore remainder will be 1!+2!+3!+4!=33

Now 33=15*2+3

Therefore remainder =3

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Blazing goIITian

Joined: 12 Apr 2008

Posts: 2717

26 Aug 2009 23:29:18 IST

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you mean 3 right ??? :)

Baban

Blazing goIITian

Joined: 19 Oct 2007

Posts: 362

27 Aug 2009 10:25:47 IST

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ya,

edison

Forum Expert

Joined: 19 Oct 2006

Posts: 7537

27 Aug 2009 11:08:13 IST

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Q) wats the remainder when 1!+2!+3!+...+175! is divided by 15?rates assured

sOL) From terms 5! and onwards all terms are divisible by 15

It is because all terms contain 3x5 = 15 as a factor

Thus the question converges to finding remainder when 15 is divided by 1! + 2! + ...+4!

Here 1! + 2! + ...+4! = 1 + 2 + 6 + 24 + 120 = 153

Thus 153/15 gives remainder as 3

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