Beethoven composed many more works than Mozart because he lived much longer

I'm not sure how you would like me to answer this but,

Mozart actually composed more symphonies that Beethoven did.

It was because he was deaf that he ended up composing less than other artists.

However, Beethoven also took lessons from Mozart. Beethoven had looked up to Mozart knowing that because of his disability, Other composers works sometimes were better than his own. (Although that's not how it went for the Moonlight Sonata and Beethoven's Sonata no. 9 Kruetzer.)

But, this statement is false.

Hope that this is the answer that you were looking for.