i just wrote a program to find the number below 100000 with the greatest amount of factors.
without looking beyond 100000, my favourite number is 83160.
it has 128 factors:
83160, 41580, 27720, 20790, 16632, 13860, 11880, 10395, 9240, 8316, 7560, 6930, 5940, 5544, 4620, 4158, 3960, 3780, 3465, 3080, 2970, 2772, 2520, 2376, 2310, 2079, 1980, 1890, 1848, 1540, 1512, 1485, 1386, 1320, 1260, 1188, 1155, 1080, 990, 945, 924, 840, 792, 770, 756, 693, 660, 630, 616, 594, 540, 504, 495, 462, 440, 420, 396, 385, 378, 360, 330, 315, 308, 297, 280, 270, 264, 252, 231, 220, 216, 210, 198, 189, 180, 168, 165, 154, 140, 135, 132, 126, 120, 110, 108, 105, 99, 90, 88, 84, 77, 72, 70, 66, 63, 60, 56, 55, 54, 45, 44, 42, 40, 36, 35, 33, 30, 28, 27, 24, 22, 21, 20, 18, 15, 14, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1