You can use Coppersmith's algorithm  (or Howgrave-Graham's  simplification) to find the factor, which will be efficient if the number of remaining bits is not too large. The PARI/GP documentation
has an explicit example. Coron, Faugère, Renault, & Zeitoun  give an improved version with impressive speed improvements, though I don't know if their code has been released or re-implemented.
 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.
 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.
 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.