Don't know if it matters but this is what the whole plant looks like.

Pretty! It's an Anthurium. Division is not necessary, quite optional. I might repot this plant soon, but don't think I would do any separating/division.

Thank you purple. I'll be getting it another inch this weekend.

Glad to respond! Don't understand your last comment about another inch?

A new pot with an extra inch in diameter.

That's 'potting up', and different than repotting. Repotting, which includes bare-rooting and root pruning that plant before transplanting into a fresh, free-draining soil, offers much greater opportunity for the plant to realize the potential Mother Nature provided it with.

It should easily go back into the same pot if you repot instead of pot up.

Al

(I thought that's what you meant, H.) Agree with Al's advice, and don't at all miss trying to pack dirt evenly around the sides of the old root ball. Haven't done that in years, and try not to "pack tightly" anyway. After doing tons of both, potting up and repotting, repotting is definitely easier for me to do, and I haven't had a bad result yet.

Slicing off a 'pancake' of circling/tangled roots at the bottom is often all that's needed. That also allows the old soil to fall off/out of the rest of the roots more easily. If you've never trimmed roots before, feel free to add another pic of the rootball out of its' pot, to get more specific advice.