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jnelson0612
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Re: If n is a positive integer and the product of all integers..

by jnelson0612 Sun Nov 06, 2011 9:38 pm

metman82 wrote:990 = 9 * 110 = 9 * 2 * 55 = 9 * 2 * 5 * 11
No other primefactors.


Yes, to be clear the prime factorization is 3 * 3 * 2 * 5 * 11.
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JJ32
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Re: If n is a positive integer and the product of all integers..

by JJ32 Fri Jun 22, 2012 1:49 pm

Sorry I understand how to get the prime factors of 990, but I am just confused of what the question is actually asking.
Is it asking for the largest prime factor or if there was another prime factor of 990 in the answer choices could that also be the answer? Just trying to figure out what the question asking?

Thanks and Regards
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Re: If n is a positive integer and the product of all integers..

by RonPurewal Sun Jun 24, 2012 8:14 pm

JJ32 wrote:Sorry I understand how to get the prime factors of 990, but I am just confused of what the question is actually asking.
Is it asking for the largest prime factor or if there was another prime factor of 990 in the answer choices could that also be the answer? Just trying to figure out what the question asking?

Thanks and Regards


the question is asking for the smallest n such that 990 is contained in the product 1 x 2 x 3 x 4 x ... x n.
if n were a smaller factor of 990 then it wouldn't work, because in that case the product 1 x 2 x 3 x 4 x ... x n wouldn't be divisible by 11, and so, a fortiori, it wouldn't be divisible by 990.
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Re: If n is a positive integer and the product of all integers..

by JJ32 Tue Jun 26, 2012 1:23 pm

RonPurewal wrote:
JJ32 wrote:Sorry I understand how to get the prime factors of 990, but I am just confused of what the question is actually asking.
Is it asking for the largest prime factor or if there was another prime factor of 990 in the answer choices could that also be the answer? Just trying to figure out what the question asking?

Thanks and Regards


the question is asking for the smallest n such that 990 is contained in the product 1 x 2 x 3 x 4 x ... x n.
if n were a smaller factor of 990 then it wouldn't work, because in that case the product 1 x 2 x 3 x 4 x ... x n wouldn't be divisible by 11, and so, a fortiori, it wouldn't be divisible by 990.



Thanks Ron. It took a while for me, but now I understand.
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Re: If n is a positive integer and the product of all integers..

by RonPurewal Thu Jun 28, 2012 3:46 am

good!
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Re: If n is a positive integer and the product of all integers..

by vijaykumar.kondepudi Sun Dec 16, 2012 8:04 am

jnelson0612 wrote:madhan, that's certainly one way to look at it. Thanks!


I fail to understand the LCM approach. LCM (Least Common Multiple) is for atleast (minimum) 2 numbers. We have only one number here: 990.

How can we conclude the answer to the question is 11 by this approach ?
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Re: If n is a positive integer and the product of all integers..

by tim Sun Dec 16, 2012 8:58 pm

the poster who mentioned LCM used the term incorrectly. you haven't missed anything.. :)
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