Question
The number 12 may be factored into three positive integers in exactly eighteen ways, these factorizations include 1x3x4, 2x2x3 and 2x3x2.
Let N be the number of seconds in a day.
In how many ways can N be factored into three positive integers?
A general method is required, not just a numerical answer.
[This question is adapted from the UK MO for Girls 2011.]
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