Which positive whole number below 100 has the most number of factors?

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Is there a mathematical function that can be done without a computer that accurately outputs the number of factors a number has, then solve this problem?
Or is there a direct way to do so?

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1 Answer

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This question adresses the question about a mathematical function which outputs the number of factors. The numbers under 100 with most factors are $60=2^2\cdot3\cdot5$, $84=2^2\cdot3\cdot7$, $96=2^5\cdot3$ and $72=2^3\cdot3^2$, which all have 12 factors.

The numbers which have more factors than any smaller number are called highly composite numbers, more info here

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