remainder vs remain

remainder is a noun but remain is not a noun.

Word	Noun	Adjective	Verb	Adverb
remainder	Yes	No	Yes	No
remain	No	No	Yes	No

remainder (noun)	remain (noun)
a piece of cloth that is left over after the rest has been used or sold
the number that remains after subtraction; the number that when added to the subtrahend gives the minuend
the part of the dividend that is left over when the dividend is not evenly divisible by the divisor
something left after other parts have been taken away

remainder (verb)	remain (verb)
sell cheaply as remainders	stay the same; remain in a certain state
	be in a certain place and not leave
	continue in a place, position, or situation
	be left; of persons, questions, problems, results, evidence, etc.