Assuming the same aspect ratio for both you can just divide 1920 by the width of the recording then multiply that by the crop factor of the sensor, MKII Full Frame would be 1920/1880 * 1.0 = 1.02 crop etc...
Well, technically CF = CF=DIAG35mm / DIAGsensor, so you should divide diagonals, not horizontals.
By the way, the resolution of the whole sensor is differ for different cameras. It is 1920 on 5dm3, but in case of 600D it's 1728.
e.g. 1880 is the real horiz. resolution of 5dm2, so no crop.