  Legendre found that the continued fraction expansion of $\sqrt N$ having odd
period leads directly to an explicit representation of $N$ as the sum of two
squares. Similarly, it is shown here that the continued fraction expansion of
$\sqrt N$ having even period directly produces a factor of a composite $N$.
Shanks' infrastructural method is then revisited, and some consequences of its
application to factorization by means of the continued fraction expansion of
$\sqrt N$ are derived.
