Which of "factors of problem" and "factors in problem" is right?

Wouldn't "problem factors" be easier?

Otherwise, it depends on the context; without any, I'd say "the factors of the problem"

I think "factors" and "problem" cannot be used together by inserting prespositon between. factor means fact, circumstance, etc that helps to produce a result. They seemed to me contradict each other.

My dictionary (OED) says one sense of "a factor" is "an element which enters into the composition of anything". So I don't think "factors of the problem" and "factors in the problem" are so bad. The corpus of "Project Gutenberg" (on-line collection of English classic books) gives 37 hits for "factors of the problem", 55 hits for "factors in the problem", and 3 hits for "problem fact