  We show analytically that the quality ($Q$) factor of magnetic and electric
Mie modes in a lossless dielectric spherical resonator with high refractive
index ($n \gg 1$) scales as $n^{2j+1}$ and $n^{2j+3}$ respectively, where $j$
denotes the multipolar order. We numerically validate these results and show
that our high-$n$ analytical relation is accurate for the dipolar modes when
$n>5$. For higher multipolar orders, the analytical relation becomes valid for
increasingly lower $n$. We study the dependence of the $Q$ factor on absorption
losses and determine a general functional form that describes the $Q$ factor
for all Mie modes for any complex refractive index. Finally, we observe that
this functional form predicts a multipolar-dependent singular value of optical
gain which gives rise to a lasing condition with an infinite $Q$ factor.
