Which bit support window 7 in core 2 duo

I have a Core2duo processor (Dell) running Windows 7 Pro 64bit just fine.

Beware of being able to add more ram though on a 64 bit OS on some of those older PC's, especially ones like the Dell I have mentioned above: 530 Inspiron where the mobo is capped at 4mb ram!!
 
A lot of old Dells that list 4GB RAM limit can run 8GB. I own 2 of them. Dell only lists RAM that they tested and sold with the systems. Often times larger modules become available late rand work just fine. Sometimes it's a BIOS update. My Optiplex 380 with just 2x RAM slots is running 8GB DDR3, and my E520 which dates back to Pentium 4 era has 8GB DDR2-800.
Here's an Inspiron 530 running 8GB DDR2 at userbenchmark.com.
http://www.userbenchmark.com/UserRun/2777581