You can use Coppersmith's algorithm [1] (or Howgrave-Graham's [2] simplification) to find the factor, which will be efficient if the number of remaining bits is not too large. The PARI/GP documentation

http://pari.math.u-bordeaux.fr/dochtml/html-stable/Arithmetic_functions.html#zncoppersmith

has an explicit example. Coron, Faugère, Renault, & Zeitoun [3] give an improved version with impressive speed improvements, though I don't know if their code has been released or re-implemented.

[1] D. Coppersmith. Finding a small root of a univariate modular equation. In U. Maurer, ed., *Advances in Cryptology* - EUROCRYPT '96, Springer, 1996, pp. 155-165.

[2] Nicholas Howgrave-Graham, Finding small roots of univariate modular equations revisited. In Cryptography and Coding (Lecture Notes in Computer Science volume 1355), 1997, pp. 131-142.

[3] Jean-Sébastien Coron and Jean-Charles Faugère and Guénaël Renault and Rina Zeitoun, A variant of Coppersmith's algorithm with improved complexity and efficient exhaustive search, Cryptology ePrint 2013/483.