The Allies divided Germany into four zones of occupation after World War II for two main reasons.  First, they did not want Germany to be unified because they did not want it to become powerful again.  Second, they did not want Germany to be ruled by just one of the Allies because they did not really trust one another (in particular, the Soviets and the Western Allies did not trust each other).

After WWII, the Allies were determined that Germany should not become powerful again.   Germany had been the main cause of WWI and WWII and the Allies did not want Germany to be able to start another major war.  One way to keep Germany weak would be to divide it up so that it would not be a unified country.  This would mean that there would be four little Germanys, all of which would be relatively weak.

The Allies also divided Germany because they did not really trust each other. The British, French, and Americans trusted each other pretty well, but the Soviets did not trust them and they did not trust the Soviets.  This meant that the Allies were not going to be able to agree to let Germany be controlled by any one Allied country.  Instead, they divided it up so that each side would control a little bit of Germany.  That way, for example, Russia could not use Germany’s resources to make it strong enough to attack France and England.