Estimating Galactic Mass of Andromeda
You have gone wrong because the radius of Andromeda is not 12250.40 arcminutes.
It is difficult to be more helpful. Possibly the units are arcseconds?

Neither do I see why you have inserted a factor of 0.5 in your second equation.
or why you have inserted $300^2$ into the third equation, when $v$ is given in km/s, so it should be $(3\times 10^5)^2$.