means The part that is left over after something has been taken away, divided, or used up — in arithmetic, the bit that won't fit evenly into a division.

from From Old French 'remaindre,' to remain, which traces back to Latin 'remanere' — 're-' (back) plus 'manere' (to stay, to abide). So at its heart it means 'what stays behind.' The same 'manere' lives on in 'mansion' (a place you stay) and 'permanent' (staying through). 'Remainder' itself entered English through Anglo-French legal language, where it named the part of an estate left to pass on after a prior interest ended — the leftover, formalized.