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# What is the least value for n?

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What is the least value for n? [#permalink]

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23 Aug 2009, 01:08
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If n is a positive integer and the product of all the integers from 1 to n, inclusive, is divisible by 990, what is the least possible value of n?

A. 8

B. 9

C. 10

D. 11

E. 12
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Re: What is the least value for n? [#permalink]

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23 Aug 2009, 01:24
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IMO D: ques says n!. divisible by 990 or 11*10*9
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Re: What is the least value for n? [#permalink]

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24 Aug 2009, 04:02
rohansherry wrote:
IMO D: ques says n!. divisible by 990 or 11*10*9

Could you please elaborate? I didn't quite get it.
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Re: What is the least value for n? [#permalink]

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24 Aug 2009, 07:45
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given that 990a = n! (whr a is multiple of 990)

now 990 = 3*3*2*5*11.......hence max value is 11..OA D
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Bhushan S.
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Re: What is the least value for n? [#permalink]

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24 Aug 2009, 12:30
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bhanushalinikhil wrote:
rohansherry wrote:
IMO D: ques says n!. divisible by 990 or 11*10*9

Could you please elaborate? I didn't quite get it.

See, here the factors of 990 = 3*3*2*5*11...

Now this divides n..... so we need to have all these factores ie. 2,3,5,11 ..then only it will divide..in n...

in n! .. the max should have 11 ....

Hope its clear now
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Re: What is the least value for n? [#permalink]

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24 Aug 2009, 20:44
rohansherry wrote:
bhanushalinikhil wrote:
rohansherry wrote:
IMO D: ques says n!. divisible by 990 or 11*10*9

Could you please elaborate? I didn't quite get it.

See, here the factors of 990 = 3*3*2*5*11...

Now this divides n..... so we need to have all these factores ie. 2,3,5,11 ..then only it will divide..in n...

in n! .. the max should have 11 ....

Hope its clear now

Thanks. This is clear. I never understood the question in the first place.
+1 for you.
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Re: What is the least value for n? [#permalink]

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28 Sep 2009, 18:48
I am not too sure i got this one..
990=11 x 3 x 3 x 5 x 2..ok..
So since we want the MINIMUM value of n we didide this by the MAXIMUM prime factor which is 11?
Am i understanding it correctly??
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Re: What is the least value for n?   [#permalink] 28 Sep 2009, 18:48
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