Why is Yantou not a factory?

As you said, "whoever thinks of the factory first, at least."

In fact, the radical of "wild goose" is really "factory". The word "Yan" can be found in Xinhua Dictionary and Modern Modern Chinese Dictionary of the most authoritative Commercial Press (see figure 1). For the convenience of readers, the word "wild goose" can also be found in "Wei" (see if you can't find "wild goose" in your dictionary, there is something wrong with your dictionary.