By what factor is the star density inside a galaxy like the Milky Way greater than the density of rogue stars in the IGM?

Perhaps $10^{18}$ times greater

The contrast in stellar density between the inside and outside of a galaxy is staggering when considering volume alone. Although the volume occupied by the intergalactic medium surrounding a galaxy is orders of magnitude larger than the volume inside the galaxy itself, the concentration of stars within the galactic boundaries is vastly higher. Calculations derived from contrasting these volumes and known stellar populations suggest this density gradient is approximately $10^{18}$ times greater inside the galaxy than in the surrounding intergalactic medium (IGM). This enormous disparity in density is the fundamental reason why isolating and observing individual unbound stars is such a formidable task for astronomy.