This question doesn't have an actual answer. Here's why:
We have a value X (doesn't matter what it equals).
pick any integer greater than one (i'll choose 3)
Y = 3*X
now Y has all the factors of X , and then one more.
Example:
X=15 (15 = 3*5, so 2 factors)
Y = 3*X (45 = 3*3*5, 3 factors (2 unique))
If you want a number with the most 'unique' factors, that doesn't work either. Just make sure the number you pick (my 3 in this case) is not factor of X to begin with.
Example: I'll chose 2 this time because 2 is not a factor of 15.
X=15 (15=3*5, 2 factors)
Y=2*X (30= 2*3*5, 3 factors (all unique))
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There is NO number with the most number of factors.
48 has the most factors..
48 has ten factors.
36 has nine factors
970200 and 900900 have 216 factors each.