There is quite a lot to say about 'common factoring.' For example, nobody knows whether there is an efficient algorithm to factor integers (where efficient dep

There is quite a lot to say about 'common factoring.' For example, nobody knows whether there is an efficient algorithm to factor integers (where efficient depends on the number of digits in the integer). However, there is an efficient algorithm to factor polynomials, and you can write all irreducible polynomials of a certain degree as factors of one mother polynomial. Moreover, being able to factor integers efficiently would allow you to break a lot of encryption schemes.