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Re: OG 11th Edition PS#241-Need explanation [#permalink]

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26 Aug 2009, 03:13

I dont understand the concept that if a no. has 3 positive divisors it is a perfect sq..HOW???WHY?? We know.. most nos. have even no. od divisors. prime nos. have exactly 2 divisors,1 and itself..

Can someone follow the same reasonung and explain the concept to me?
_________________

Re: OG 11th Edition PS#241-Need explanation [#permalink]

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26 Aug 2009, 05:31

tejal777 wrote:

I dont understand the concept that if a no. has 3 positive divisors it is a perfect sq..HOW???WHY?? We know.. most nos. have even no. od divisors. prime nos. have exactly 2 divisors,1 and itself..

Can someone follow the same reasonung and explain the concept to me?

Let's see.. the number N has EXACTLY 3 devisors: 1, x and itself N. (1<x<N) If we devide N by x, we get ... another x. (no 1, no N, no another y - as y is fourth devisor). Any N/x=x 4/2=2 ... 9/3=3... This x is a prime, coz if not then N would have more then 3 devisors

Re: OG 11th Edition PS#241-Need explanation [#permalink]

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26 Aug 2009, 11:54

let 1, n1, n are the 3 factors of n, then n^2 will have factors:-

1,n1,n1^2,n,n^2.

Consider n^2 as n * n So, if n1 is a factos of n then , it will also be a factor of n^2. Similarly, we have 2 n's in n^2, so n1^2 will also be a factor of n^2.