Question 1132327
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I'd reformulate this problem in this way


<pre>
    What are the numbers that are less than 100 and have maximal number of {{{highlight(cross(factors))}}} <U>divisors</U>? 
    How many different prime {{{highlight(cross(factors))}}} <U>divisors</U> do these numbers have?
</pre>
to make the formulation more precise (and more professional).



<U>Solution</U>


<pre>
The number  96 = {{{2^5*3}}}  has  (1+5)*(1+1) = 6*2 = 12 divisors  

    1, 2,  4,  8, 16, 32,

    3, 6, 12, 24, 48, 96.


It has two prime divisors  2  and  3.



The number  60 = {{{2^2*3*5}}}  has  (1+2)*(1+1)*(1+1) = 3*2*2 = 12 divisors  

    1,   2,   4, 

    3,   6,  12,

    5,  10,  20,

    15, 30,  60.


It has three prime divisors  2, 3 and 5.
</pre>


I didn't check that these numbers provide the maximum number of divisors, but I think it is so.


Having this &nbsp;<U>HINT</U> &nbsp;from me, &nbsp;you may check/(or disprove) it on your own.


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<U>Addition</U> :  


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1) &nbsp;&nbsp;I was right with the numbers 60 and 96.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2) &nbsp;&nbsp;The numbers &nbsp;84 &nbsp;and &nbsp;90 &nbsp;also have &nbsp;12&nbsp; divisors each.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See the table of divisors in this Wikipedia article

<pre>
        https://en.wikipedia.org/wiki/Table_of_divisors#1_to_100
</pre>