Since this is an OEM or pre-built computer, it is a little different when finding compatible processors for the computer, the manufacturer of the device could have chosen an specific list of processors that would work with the system.
After doing my research, I was not able to find this list; however, a list of compatible processors for the Motherboard is present. (check links below)
Now, even though this list is available, my recommendation would be to double check with emachines to request a list of compatible CPUs, just to make sure they certainly will work.
I look forward to your outcome on this for future references.