I count 48 EVEN divisors:
7! =5,040 = 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 24 | 28 | 30 | 36 | 40 | 42 | 48 | 56 | 60 | 70 | 72 | 80 | 84 | 90 | 112 | 120 | 126 | 140 | 144 | 168 | 180 | 210 | 240 | 252 | 280 | 336 | 360 | 420 | 504 | 560 | 630 | 720 | 840 | 1008 | 1260 | 1680 | 2520 | 5040 (48 divisors)
