What do you mean by "factory reset"
That would mean (to me) erasing the hard drive as a first step, then reinstalling the original system that shipped on your MBAir.
So, if you want to do that, boot to Internet Recovery (which is probably where you were)
Run Disk Utility, erase the hard drive. Quit Disk Utility to return the main screen, then run Reinstall OS X.
Now Mountain Lion will install, because your hard drive is blank (erased).