Beowulf and Gilgamesh Motives

I think in Gilgamesh and Beowulf, both characters fight their monster for something in return. Gilgamesh wants to gain immortality, and the only way to achieve that is to impress the gods. In Beowulf, Beowulf wants to achieve fame and glory for being a war hero and great leader. Although Beowulf has good intentions of fighting to save Herot from Grendel, I believe a part of him wants to be recognized as a hero, and he wants to gain treasure. Whether it is immortality or fame, Gilgamesh and Beowulf are somewhat similar through their motives of killing their monster.