Dissecting the monster: (2016)

Calculus Level pending

The number 2016 is to be dissected into some parts so that the product of the parts is maximized. If the number of such parts be \( \phi \), then find its value.

Details and Assumptions:

While evaluating \(\phi\) you might come across one or more than one, integer or non-integer answers, thus, choose the nearest integer.

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