The creditable H.W. Fowler described "factor" as "one of those words . . . which are so popular as thought-saving reach-me-downs that all meaning is being rubbed off them by constant use." Fowler's Modern English Usage (2d ed. p. 184).
When I think of factoring in the legal sense, I think of someone who is engaged in the business of purchasing accounts receivable from her customers at a discount, collecting the receivables, and making a profit on the difference between the discounted rate paid and the receivables collected. See Moore v. Hill, 188 Cal. App. 4th 1267 (2010). However, the California legislature has a different view of who is a factor:
A factor is an agent who, in the pursuit of an independent calling, is employed by another to sell property for him, and is vested by the latter with the possession or control of the property, or authorized to receive payment therefor from the purchaser.
Cal. Civ. Code § 2026. This definition of "factor" as agent is not peculiar to California legal jargon. In William Shakespeare's Cymbeline, the wily Iachimo describes himself as such to Princess Imogen:
Some dozen Romans of us and your lord—
The best feather of our wing—have mingled sums
To buy a present for the emperor
Which I, the factor for the rest, have done
In France: 'tis plate of rare device, and jewels
Of rich and exquisite form; their values great;
And I am something curious, being strange,
To have them in safe stowage: may it please you
To take them in protection?
Act I, Scene 6 (Iachimo is setting up his scheme to get himself into Imogen's bedchamber by secreting himself in a trunk containing the valuables that he claims to have purchased for the emperor).
A factor, as defined by Civil Code Section 2026, is often referred to as a "commission merchant", a term used, but not defined, in the Civil Code (See Sections 2081, 2081.1, 2081.4, and 2081.5). Oddly, the California Food & Agricultural Code uses both terms. See, e.g., Cal. Food and Agricultural Code Section 27052 ("Agent" includes bailee, broker, commission merchant, factor, auctioneer, solicitor, consignee, and any other person that is acting upon the express or implied authority of another.").
The relationship between "agent" and "factor" is etymological. Both are derived from Latin verbs (ago and facio) that mean to do something. Thus, agents and factors are persons who do something for another.