The word artifact (also artefact) takes its original meaning from the Latin ars (art) and the neuter past participle factum of the verb facere (to make). Thus something made by human construction or something artificial. The OED finds the earliest usage from Samuel Taylor Coleridge's Literary Remains:
Well! a lump of sugar of lead [lead acetate (Pb(CH3COO)2)] lies among
other artefacts on the shelf of a collector; and with it a label,
“Take care! this is not sugar, though it looks so, but crystallized
oxide of lead, and it is a deadly poison.”
So the poison is one artefact among a number of artefacts, and in such a countable context the plural is required. The OED supplement finds a second, later (from 1908) meaning in "technical and medical use" meaning some extraneous "product or effect" not found in the natural state of something under investigation. The examples taken from the 1961 British Medical Dictionary include from histology, the contamination from reagents; from EEG studies, signals originating from electrical sources other than brain activity; and in dermatology, self-inflicted skin damage.
In the later usage, artifact is a collective, non-countable noun, and the British Medical Dictionary illustrates the variety of artifact. But a non-countable usage isn't compatible with numeration, so the presence of the phrasing number ... of precludes the singular.