Estimating Galactic Mass of Andromeda So I need to estimate the mass of the andromeda galaxy using: 
$$ M = \frac{v^2r}{G}$$
where $v$ is the rotational velocity, $r$ the galaxy's radius and $G$ Netwon's gravitational constant. I'm told the following:


Distance (m) = 2.403×$10^{22}$ 
Radius (arcmin) = 12250.40
Velocity (km/s) = 300


I went so far as to convert the radius: 
$$ \frac{12250.4}{60*57.3} = 3.563\ rad$$
then, calculated the radius:
$$0.5*3.563*2.403\times10^{22} = 4.2757\times10^{22}$$
Then subbed into original formula to get:
$$\frac{ 4.2757\times10^{22} \times 300^2}{G} = 1.7595\times10^{36} kg$$
It should be $2\times10^{42}kg$. where have I gone wrong?
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 $(3\times 10^5)^2$.