Hi, "factorization" is just taking a thing and expressing it as a product of simpler things. For example, a composite integer is a product of powers of primes.

In probability theory, we get a simple factorization via the chain rule of probability. If we have independence, some things drop out, but factorization is basically intellectually content-free. Of course, I also think Bayes rule is an intellectually content-free consequence of the chain rule of probability. And of course this may be hindsight bias operating...

You are welcome to message or email me if you want to talk about it more.