  A finite-dimensional analogue of the known Gordon-Lewis constant of a Banach
space X is introduced; in its definition are used only finite rank operators.
It is shown that there exist Banach spaces such that the standard Gordon-Lewis
constant of X is finite and its finite-dimensional analogue GLfin(X) is
infinite. Moreover, for any Banach space X of cotype 2 its finite-dimensional
constant GLfin(X) is finite too.
