Where does the word cloth come from?

Before i write down my answer, i must say that this is a guess.
The mythological beings known as The Fates, there were three, their names are Clotho Lachesis and Atropos. Clotho spins the thread of life, Lachesis measures it, and Atropos cuts it. Thus saying when you are born, and how long you will live. There are more details but I'm skipping them because they are irrelevant. The first one, Clotho. Cloth. So my guess is that the word comes from Clotho, whom spins the thread of life.