I have learnt that “part” is a countable noun, so both “a part of sth” and “parts of sth” are acceptable. But I sometimes read of “part of” used in some contexts as in the following example:
Justice is part of the complex machinery of the law.
It would also be possible to write “a part of” there, but in the English of native speakers, the article is often left out, and we just say “part of”. It’s perfectly acceptable, and it’s more common than “a part of”.