  In his 1984 AMS Memoir, George Andrews defined the family of $k$--colored
generalized Frobenius partition functions. These are denoted by $c\phi_k(n)$
where $k\geq 1$ is the number of colors in question. In that Memoir, Andrews
proved (among many other things) that, for all $n\geq 0,$ $c\phi_2(5n+3) \equiv
0\pmod{5}.$ Soon after, many authors proved congruence properties for various
$k$--colored generalized Frobenius partition functions, typically with a small
number of colors.
  Work on Ramanujan--like congruence properties satisfied by the functions
$c\phi_k(n)$ continues, with recent works completed by Baruah and Sarmah as
well as the author. Unfortunately, in all cases, the authors restrict their
attention to small values of $k.$ This is often due to the difficulty in
finding a "nice" representation of the generating function for $c\phi_k(n)$ for
large $k.$ Because of this, no Ramanujan--like congruences are known where $k$
is large. In this note, we rectify this situation by proving several infinite
families of congruences for $c\phi_k(n)$ where $k$ is allowed to grow
arbitrarily large. The proof is truly elementary, relying on a generating
function representation which appears in Andrews' Memoir but has gone
relatively unnoticed.
