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ISI2014-DCG-69

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Option A) 18 is correct

$1440=2^5*3^2*5^1$

No of factors of $1440$= $(5+1)(2+1)(1+1)$=$36$

1440 is not a perfect square so no of ways it can be written as product of two factors = $36/2=18$

If n is not a perfect square then no of ways it can be written as product of factors= (# of factors of n)/2

If n is a perfect square then no of ways it can be written as product of factors = (# of factors of n -1)/2

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If n is a perfect square then no of ways it can be written as product of factors = (# of factors of n -1)/2 

 

This is true only when the question explicitly says that factors have to be different otherwise the first formula just works fine. take the perfect square 36 as an example..

 

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