I don't think it's productive to attempt to determine the part of speech of this word - it's neither, since it modifies neither a noun nor a verb. necesse/necessum est, opus est, ūsus est and oportet are all predicative expressions that are semantically indivisible, forming the predicate together. If you classify necesse as an adjective, you'd have to ...
Lewis & Short, Gaffiot, Georges and Forcellini agree that it is an adjective. Oxford appears to be alone with its opinion that it is an adverb, and I wonder if the entry itself has anything to say about that. Aliquid alicui necesse est is a very common expression, and as Draconis has explained, a neuter adjective hardly seems out of place here.
Spīrā-re necesse est homin-ī
breathe-INF necessary be.3SG.PRES human-DAT.SG
Breathing is necessary for a human.
I would call it an adjective without a qualm. It's linked to a nominal (an infinitive verb) by a copula, and that's a syntactic context that adjectives appear in:
Errā-re humān-um est
err-INF human-N.SG.NOM be.3SG.PRES
To err is human.
Since it doesn't appear in standard classical dictionaries, Du Cange, DMLBS, or Hoven's Dictionary of Renaissance Latin, it is most likely not a Latin word, though it is impossible to disprove it entirely.
If it was ever intended to reference Latin, it might have been an ill-formed adverb, as Intus Justitia is intelligible as "justice within [our ...
It's Neo-Latin, the perfect passive participle of recudere, which itself likely was coined on cudere, and it means "printed" or "reprinted."
So sometimes you'll see accurate denuo recusus, which means "accurately printed again."
II. Transf. (of metals), to prepare by beating or hammering, to forge; of money, to ...
According to Johann Ramminger's Neo-Latin Word List, recudere means "to print" or "to reprint."
It is doubtlessly derived from classical cudere "to strike, to stamp or coin money."
Thus, denuo recusus means "newly printed."
The quotient is quotus, the remainder is residuum.
This textbook titled Elementa arithmeticae singularis et universalis lays it out in very simple terms:
Dividere est ex producto duorum factorum et ex uno eorundem alterum invenire.
Productum cognitum vocatur dividendus.
Factor cognitus vocatur divisor.
Factor incognitus vocatur quotus.
(Click the link and ...