To quote from this page:
FACTOR and FACTOR ANALYSIS in PSYCHOMETRICS. The first factor analysis
was in Charles Spearman’s “General intelligence,” objectively
determined and measured American Journal of Psychology, 15, (1904),
201-293. However the term factor came later; see e.g. Spearman’s “The
theory of two factors,” Psychological Review, 21, (1914), 101-. The
term factor analysiscame into circulation in the 1930s. The OED quotes
from “Multiple Factor Analysis,” Psychological Review, 38, (1931),
406-427 by Louis L. Thurstone: “It is the purpose of this paper to
describe a more generally applicable method of factor analysis which
has no restrictions as regards group factors and which does not
restrict the number of general factors that are operative in producing
the correlations.”