Uh...one of the two parts is wrong here. You either don't have an i7 4770k or you don't have a 1155 motherboard.
With an LGA 1155 motherboard, the best you can get is a 3770k, but if you're absolutely sure you have a 4770k, then you own an LGA 1150 motherboard.
That said, GPUs aren't much about memory compatibility, but rather about bottlenecking issues and PCIe revision. It's mostly a matter of how fast data gets processed by the system for the card.
Get yourself an analysis software such as Speccy (very basic, but will do the trick I think) and post your full specifications, please, as well as the GPU you're thinking to buy.