The internal energy is an extensive quantity. The temperature T is an intensive property, independent of the size of the system. It follows that the entropy S is an extensive property.

Why entropy is intensive property?

Re: Why is entropy extensive? An extensive property is dependent on size (or mass), and like you said, entropy = q/T, and q in itself is dependent on the mass, so therefore, it is extensive. Mass is an extensive property. An example of an intensive property would be density of water.

Is change in entropy an intensive property?

Entropy is an intensive property.