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# A computer is programmed to multiply consecutive even integers 2*4*6*8

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Intern
Joined: 26 Jul 2016
Posts: 28
Location: India
Concentration: Operations, Entrepreneurship
Schools: Tepper '19
GPA: 3.69
WE: Analyst (Manufacturing)
A computer is programmed to multiply consecutive even integers 2*4*6*8  [#permalink]

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Updated on: 01 Sep 2016, 09:13
5
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:04) correct 46% (02:16) wrong based on 105 sessions

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A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?

A) 22
B) 38
C) 62
D) 122
E) 672

Originally posted by yashrakhiani on 01 Sep 2016, 08:30.
Last edited by Bunuel on 01 Sep 2016, 09:13, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
Math Expert
Joined: 02 Aug 2009
Posts: 8792
Re: A computer is programmed to multiply consecutive even integers 2*4*6*8  [#permalink]

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01 Sep 2016, 08:40
3
2
yashrakhiani wrote:
A computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 2013, What is the value of n?

Factorise 2013.. 3*11*61..
So n has to be a multiple of largest prime number,61..
So n=2*61=122..

Hope this helps you
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Joined: 13 Oct 2016
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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8  [#permalink]

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30 Oct 2016, 03:35
2
yashrakhiani wrote:
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?

A) 22
B) 38
C) 62
D) 122
E) 672

Same logic but with application of factorials.
2*4*6*8*...*n = 2(1*2*3*4*...n/2) = 2*(n/2)!
Now we have: 2*(n/2)!/2013=2*(n/2)!/(3×11×61)
For the expression 2*(n/2)! To be divisible by 2013 min value of n/2 should be 61.
So n/2=61 => n=122
Senior Manager
Joined: 18 Dec 2017
Posts: 307
Re: A computer is programmed to multiply consecutive even integers 2*4*6*8  [#permalink]

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11 Apr 2020, 10:18
2013=3×11×61
So we need 61 in the given series which will come in 2×61=122
Till 122, 11 and 3 will already be covered.

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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8   [#permalink] 11 Apr 2020, 10:18