I wrote out all the factors of all the numbers from 1 to 100 and counted them.
the number 90 has the most factors under 100
Of the numbers up to 50, 48 has the most factors.
48 does.
180
720 has 30 factors.
I am not sure but I suggest 7200, with 54 factors.
840
Eight has.
360, 420 and 480 each have 24 factors.
The numbers 60, 72, 84, 90, and 96 each have 12 factors.
100... pretty much most high numbers...
45, 63, 75 and 99 each have six factors.