Can i hook my printer to a wireless router and connect to it wirelessly?

yes can, depending on wireless router.

2840 has ethernet jack, meaning can plug router , assign ip address can use print printer on network. there few things though must work in favor:

1.) wireless router must have open ethernet port (so must wireless/wired combination router , not access point. printer cannot connect wireless-ly anything.
2.) wired network , wireless network should on same subnet (they are).

once you've done that, install printer would, when using install wizard on cd, sure select "connected via network" installation option.

here pdf manual:
http://bizsupport.austin.hp.com/bc/docs/...

page 297 has exact install steps model.

edit: guy below me right well, assuming have more 1 computer.

printer hp color laserjet 2840

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