Is it necessary to repeat the ghusl if one discovers they were in a state of janabah after performing ghusl and prayer, and did not intend the ghusl of janabah during the first ghusl?

If someone prayed while in a state of major ritual impurity (janabah) unknowingly, and then realized it, they must perform ghusl (ritual bath) with the intention of removing the janabah and repeat the prayer. This is because ghusl performed merely for cleanliness or cooling down does not remove janabah, for "deeds are by intentions."