Unfortunately NO! The factorization is a hard problem on which many cryptosystems or crypto-protocols are built, and is known as the IFP problem, compared to DLP (Discrete Log Problem) in intractability.
Even in the case where $M= 10^{10}$ computers are available, you can't accelerate the resolution of the IFP by M, unless you invent a new and clever algorithm (to be highly parallelisable). Trying a brute force attack, even on modest modulus length of 512 bit is out of range and would cost billion of years. The best algorithm known today for achieving this task (it succeeded breaking up to 768 bit on a large network of computers in some months) is the Number Field sieve or NFS for short. Roughly speaking it's based on two main steps and requires a huge amount of memory storage.
- Sieving Step: can be performed in parallel on a large network of computers. But unfortunately need a large amount of memory storage,
- Reduction Step: a linear algebra reduction as a Gaussian elimination or refinement as the Bloc Lanczos reduction, which need to solve a huge matrix and can't be parallelisable.
NB: I conclude that factorization Algorithms, is a central and vital question for Cryptography. Don't ignore it! Take a look over the web on the works done in this field, to measure the importance of this kind of question.
