Results on factorization (through linear operators) of polynomials and holomorphic mappings between Banach spaces have been obtained in recent years by several authors. In the present paper, we obtain a factorization result for differentiable mappings through compact operators. Namely, we prove that a mapping
f
:
X
→
Y
f:X\to Y
between real Banach spaces is differentiable and its derivative
f
′
f’
is a compact mapping with values in the space
K
(
X
,
Y
)
{\mathcal K}(X,Y)
of compact operators from
X
X
into
Y
Y
if and only if
f
f
may be written in the form
f
=
g
∘
S
f=g\circ S
, where the intermediate space is normed,
S
S
is a precompact operator, and
g
g
is a Gâteaux differentiable mapping with some additional properties. We also show that if
f
′
f’
is uniformly continuous on bounded sets and takes values in
K
(
X
,
Y
)
{\mathcal K}(X,Y)
, then
f
′
f’
is compact if and only if
f
f
is weakly uniformly continuous on bounded sets.