  For every natural number $n$ and a fixed prime $p$, we prove a new congruence
for the orbifold Euler characteristic of a group. The $p$-adic limit of these
congruences as $n$ tends to infinity recovers the Brown-Quillen congruence. We
apply these results to mapping class groups and using the Harer-Zagier formula
we obtain a family of congruences for Bernoulli numbers. We show that these
congruences in particular recover classical congruences for Bernoulli numbers
due to Kummer, Voronoi, Carlitz, and Cohen.
