Is the regular steps needed to hatch something divided by whatever number, or is a specific amount of steps taken off but not divided? Or is it something else?
Well, according to Bulbapedia, Hatching O-Power Lv. 1 makes eggs hatch 1.25 times as fast, Hatching O-Power Lv. 2 makes eggs hatch 1.5 times as fast, and Hatching O-Power 3 makes eggs hatch 2 times as fast.
While the power is activated, it will take less time to hatch an egg. here is the chart
Lv 1 power- 1.25 as quick.
lv 2- 1.5
lv 3- 2