Home » Ask & Discuss » Mathematics
« Back to Discussion

Algebra

Blazing goIITian

Joined:	19 Mar 2012
Post:	421

8 Apr 2012 20:57:55 IST

8 People liked this

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)

KAREENA

Blazing goIITian

Joined: 19 Mar 2012

Posts: 421

8 Apr 2012 21:49:41 IST

Like 0 people liked this

hi! i got the answer.

HIMANSHU MEENA

New kid on the Block

Joined: 8 Apr 2012

Posts: 11

8 Apr 2012 23:20:44 IST

Like 0 people liked this

PLZ DONT WASTE UR TIME HERE :D

Akash

Blazing goIITian

Joined: 7 Jan 2009

Posts: 364

9 Apr 2012 01:28:27 IST

Like 0 people liked this

20 divides every number from 5! giving remainder 0. So 1!+2!+3!+4!=25 when divide by 20 gives 5 as remainder.

M kartik

Cool goIITian

Joined: 29 Mar 2012

Posts: 62

25 Apr 2012 15:18:51 IST

Like 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.

J GANESHKUMAR

New kid on the Block

Joined: 25 Jan 2010

Posts: 18

25 Apr 2012 16:05:07 IST

Like 2 people liked this

remainder is 13...1!+2!+3!+4! = 3333/20 gives remainder as 13

J GANESHKUMAR

New kid on the Block

Joined: 25 Jan 2010

Posts: 18

25 Apr 2012 16:05:54 IST

Like 2 people liked this

IT IS 33/20 WHICH HAS REAMINDER 13

M kartik

Cool goIITian

Joined: 29 Mar 2012

Posts: 62

27 Apr 2012 11:16:11 IST

Like 0 people liked this

yeah..yeah..please friends hit 'like' for my answer.

M kartik

Cool goIITian

Joined: 29 Mar 2012

Posts: 62

27 Apr 2012 12:02:40 IST

Like 0 people liked this

oh so rude i solved it first i deserve a like!

souradipta

Cool goIITian

Joined: 21 Apr 2012

Posts: 57

27 Apr 2012 12:13:13 IST

Like 0 people liked this

5! onwards every valuse is divisible by 20so 1+2+6+2433-20=13 remainder

boywholived

Scorching goIITian

Joined: 10 Feb 2012

Posts: 262

27 Apr 2012 12:22:52 IST

Like 0 people liked this

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)

boywholived

Scorching goIITian

Joined: 10 Feb 2012

Posts: 262

27 Apr 2012 12:23:10 IST

Like 0 people liked this

Isn't it guys

boywholived

Scorching goIITian

Joined: 10 Feb 2012

Posts: 262

27 Apr 2012 12:23:24 IST

Like 0 people liked this

M kartik

Cool goIITian

Joined: 29 Mar 2012

Posts: 62

27 Apr 2012 12:29:16 IST

Like 0 people liked this

what?

GOPAKUMAR

Scorching goIITian

Joined: 18 Mar 2010

Posts: 278

27 Apr 2012 12:31:05 IST

Like 2 people liked this

Rushi Vyas

New kid on the Block

Joined: 27 Apr 2012

Posts: 27

27 Apr 2012 12:35:35 IST

Like 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.......

Thanks... LIKE IF YOU SUPPORT

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team