Answer
The factor is about 3.3 million.
Work Step by Step
Calculate the number of conduction electrons in 1 mole of pure silicon.
$$N_{Si}=\left(\frac{28.09\times10^{-3}kg/mol}{2330kg/m^3}\right)(10^{16}electons/m^3)=1.2\times10^{11}$$
Now find the extra conduction electrons provided if the silicon is doped.
$$N_{doping}=\left(\frac{6.02\times10^{23}atoms}{1.5\times10^6}\right) =4.0\times10^{17}$$
Take the ratio of the two numbers of conduction electrons to find the factor by which the density of conduction electrons is increased.
$$\frac{ N_{doping}}{N_{Si}}=\frac{4.013\times10^{17}}{1.206\times10^{11}}\approx 3.3\times10^6$$