I've completely forgotten the number.

Literal

Number [object-を] cleanly-thoroughly forgot-[completive-てしまった].

奇麗さっぱり (綺麗さっぱり) is a set adverbial phrase literally 'cleanly and refreshingly,' used metaphorically to mean 'completely, without a trace.' ~てしまった here carries the regretful-completion nuance — the forgetting is both thorough and unfortunate. The subject ('I') is omitted per standard Japanese practice.