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The factorial (!) of a positive integer n denotes the product of all

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The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 29 Oct 2018, 05:37
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The factorial (!) of a positive integer n denotes the product of all integers from 1 to n, inclusive. If k = 1! + 2! + 3! + . . . + p! , where p is a prime number greater than 10, what is the remainder when k is divided by 4?

A. 0
B. 1
C. 2
D. 3
E. 9
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Re: The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 29 Oct 2018, 06:20
Apart from 1! , 2! and 3! , everything else will be divisible by 4.
1+2+6=9
Remainder = 1
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Re: The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 08 Nov 2018, 18:23
pandeyashwin wrote:
Apart from 1! , 2! and 3! , everything else will be divisible by 4.
1+2+6=9
Remainder = 1



3!=6
r(6/4)=2
r(2!/4)=2
r(1!/4)=1

1+2+2=5

r(5/4)=1

is my method correct?
Manager
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Re: The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 08 Nov 2018, 18:40
Mansoor50 wrote:
pandeyashwin wrote:
Apart from 1! , 2! and 3! , everything else will be divisible by 4.
1+2+6=9
Remainder = 1



3!=6
r(6/4)=2
r(2!/4)=2
r(1!/4)=1

1+2+2=5

r(5/4)=1

is my method correct?

yes it's the same approach. (Adding remainders instead of the numbers)
Manager
Manager
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B
Joined: 29 May 2017
Posts: 130
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 08 Nov 2018, 18:46
pandeyashwin wrote:
Mansoor50 wrote:
pandeyashwin wrote:
Apart from 1! , 2! and 3! , everything else will be divisible by 4.
1+2+6=9
Remainder = 1



3!=6
r(6/4)=2
r(2!/4)=2
r(1!/4)=1

1+2+2=5

r(5/4)=1

is my method correct?

yes it's the same approach. (Adding remainders instead of the numbers)


thanks
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Joined: 13 Mar 2018
Posts: 9
Re: The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 09 Nov 2018, 23:48
Can someone kindly explain why everything apart from 1!, 2! and 3! is divisble by 4. May someone please share formula if any
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Posts: 223
Re: The factorial (!) of a positive integer n denotes the product of all  [#permalink]

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New post 09 Nov 2018, 23:52
2
SWAPNILP wrote:
Can someone kindly explain why everything apart from 1!, 2! and 3! is divisble by 4. May someone please share formula if any


2! = 2x1
3! = 3x2x1

4! = 4x3x2x1
5! = 5x4x3x2x1
6! = 6x5x4x3x2x1
and so on
GMAT Club Bot
Re: The factorial (!) of a positive integer n denotes the product of all &nbs [#permalink] 09 Nov 2018, 23:52
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The factorial (!) of a positive integer n denotes the product of all

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