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I understood solution till no of factor of are 75 

can some explain me last step?

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 Let the representation be X * Y, if there is are odd number of factors there will be a representation of the form X * X(32400 = 180 * 180). Also, we don't have to count the representations X * Y and Y * X twice.

Ref: https://math.stackexchange.com/questions/525935/why-perfect-square-has-odd-number-of-factors 

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