Ah yes, the factors. Factors are, indeed, agents who buy and sell goods on commission for a principal. Historically, factors were useful intermediaries who could do the buying and selling for a principal who couldn’t be at an important location, they warehoused people’s goods, they guaranteed credit, etc. The word factory actually originally meant a factor’s place of business, a trading post.
However, I think you’re getting too focused in on the idea of them being royal officers. Let’s take a look at the passage from Tyrion IV of ACOK as a whole:
“The Keepers of the Keys were his, all four. The
King’s Counter and the King’s Scales were men he named. The officers in charge
of all three mints. Harbormasters, tax farmers, custom sergeants, wool factors,
toll collectors, pursers, wine factors; nine of every ten belonged to
Littlefinger.”
These are all men who are loyal to Littlefinger, but not all of them are royal officials. The Keepers of the Keys, the King’s Counter and the King’s Scales, the harbormasters, and customs sergeants are government officials. But tax farmers are private citizens who buy the right to tax from the government; pursers are the officers on ships responsible for handling supplies and repairs, and factors are commercial intermediaries.
All of them rely on Littlefinger in different ways, as I discuss here. The royal officials and tax farmers bribed him to get their posts and now pay him kickbacks, but the wool factors are tied to him because Littlefinger “bought wool from the north…stored it, moved it, dyed it, sold it” and thus controls a good deal of the textile trade, and the wine merchants are tied to him because there’s a royal excise tax on wines. And the pursers are tied to him because Littlefinger has close ties to King’s Landing merchants who supply the merchant ships.
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