A real arrangement of affine lines is a finite family
A
\mathcal {A}
of lines in
R
2
{{\mathbf {R}}^2}
. A real arrangement
A
\mathcal {A}
of lines is said to be factored if there exists a partition
Π
=
(
Π
1
,
Π
2
)
\Pi = ({\Pi _1},{\Pi _2})
of
A
\mathcal {A}
into two disjoint subsets such that the Orlik-Solomon algebra of
A
\mathcal {A}
factors according to this partition. We prove that the complement of the complexification of a factored real arrangement of lines is a
K
(
π
,
1
)
K(\pi ,1)
space.