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Algebra

Blazing goIITian

 Joined: 19 Mar 2012 Post: 421
8 Apr 2012 20:57:55 IST
8 People liked this
15
547
REMAINDER
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Find the remainder when 1!+ 2!+3!................47! is divided by 20.

Comments (15)

Blazing goIITian

Joined: 19 Mar 2012
Posts: 421
8 Apr 2012 21:49:41 IST
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hi! i got the answer.

New kid on the Block

Joined: 8 Apr 2012
Posts: 11
8 Apr 2012 23:20:44 IST
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PLZ DONT WASTE UR TIME HERE :D

Blazing goIITian

Joined: 7 Jan 2009
Posts: 364
9 Apr 2012 01:28:27 IST
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20 divides every number from 5! giving remainder 0. So 1!+2!+3!+4!=25 when divide by 20 gives 5 as remainder.

Cool goIITian

Joined: 29 Mar 2012
Posts: 62
25 Apr 2012 15:18:51 IST
1 people liked this

upto 4! there are are no zeroes.so after 4! it will divide every numder.so answer ois 1!+2!+3!+4!=32.so reaminder is 12. if 0! is included then 13.

New kid on the Block

Joined: 25 Jan 2010
Posts: 18
25 Apr 2012 16:05:07 IST
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remainder is 13...1!+2!+3!+4! = 3333/20 gives remainder as 13

New kid on the Block

Joined: 25 Jan 2010
Posts: 18
25 Apr 2012 16:05:54 IST
2 people liked this

IT IS 33/20 WHICH HAS REAMINDER 13

Cool goIITian

Joined: 29 Mar 2012
Posts: 62
27 Apr 2012 11:16:11 IST
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yeah..yeah..please friends hit 'like' for my answer.

Cool goIITian

Joined: 29 Mar 2012
Posts: 62
27 Apr 2012 12:02:40 IST
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oh so rude i solved it first i deserve a like!

Cool goIITian

Joined: 21 Apr 2012
Posts: 57
27 Apr 2012 12:13:13 IST
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5! onwards every valuse is divisible by 20so 1+2+6+2433-20=13 remainder

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
27 Apr 2012 12:22:52 IST
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I have seen some reply that had added the terms and then found out the remainder the better way would be to just add the remainders obtainded.so .1+2+6+4=13(mod 20)

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
27 Apr 2012 12:23:10 IST
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Isn't it guys

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
27 Apr 2012 12:23:24 IST
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reply

Cool goIITian

Joined: 29 Mar 2012
Posts: 62
27 Apr 2012 12:29:16 IST
0 people liked this

what?

Scorching goIITian

Joined: 18 Mar 2010
Posts: 278
27 Apr 2012 12:31:05 IST
2 people liked this

13

New kid on the Block

Joined: 27 Apr 2012
Posts: 27
27 Apr 2012 12:35:35 IST
1 people liked this

1! + 2! + .... + 47!

= 1 + 2 + 6 + 24 + 120.... + 47 !

= 1 + 2 + 6+ 24 + 1*2*3*(4*5) + 1*2*3*(4*5)*6 + .... + 1*2*3*(4*5)*....*47

= 1 + 2 + 6 + 24 + 20 ( 1*2*3 + 1*2*3*6 + ...... + 1*2*3*6*.....*47)

= (1 + 2 + 6 + 24) + 20m  [m belongs to N]

20m is divisible by 20 as 20 , m belongs to N

= 33 + 20m

= 13 + 20 + 20m

= 13 + 20(m+1)

here, m+1 belongs to N so .. 20(m+1)

so the ans. is 13.......

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