The Flyweight design pattern has a Factory, but it does not follows the Factory pattern, so why it is called Factory?

I mean:

1. The Factory method has a main purpose/method and the creation of the object inside of the method depends on the subclass that inherits it.
2. The Abstract Factory has Factories that creates objects based on their divisions/families.
3. The Simple Factory has a method that, depending on a condition, it creates a new object with some specific properties/configuration

So:

• Why it’s called Factory on the Flyweight pattern if it acts as a cache and not a creation method?