See here [0]. Generally on firmware 3.55 or older CFW can be installed directly. On consoles that came from factory with 3.55 or older but were updated CFW can be installed using PS3Xploit. Consoles that came with 3.56 or newer cannot be fully jailbroken, but some homebrew features can be utilized on OFW through PS3HEN [1]

[0] https://www.reddit.com/r/ps3homebrew/wiki/index [1] https://www.psx-place.com/threads/update-4-87-ps3hen-v3-0-2-...