It's not trivial though - it's not easy to 'push air through a HEPA filter' - you need to shop for a motor, blades, and filter more than simply fan (comprising motor and blades) and filter really. Or at least you need to be aware and get a suitably beefy fan - I think $50 is a hard budget to hit just for that reason. Or at least it is if you don't have easy access to cheap 'box fans' that are for some reason so prevalent in North America (what's their usual use?).

You can spend a lot of money on just a fan, it's not just air purifier marketing nonsense.