The best replacement for factorization is gaussian elimination.

The best alternatives to factorization are rated as following:
★★★★★  gaussian elimination

Your alternative for factorization is not listed? Suggest!
Speaking about factorization, one probably shouldn't forget about factor trees.

Other search terms related to factorization and their ratings are:
★★★★★ factor trees
★★★ using exponents
★ common factor
★ lcm
You have in mind a companion for factorization and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of factorization in all years. Click on graph for more.
factorization
gaussian elimination