Even introducing the factors of 5 creates centuries of complications (temperament) that caused us to finally give up and throw out all the integer factors, replacing them with the twelfth root of 2.

(Anyone who wants to reply saying that factors of 7 explain "blue notes", please be specific about how this works. I think this is a fictitious idea in music theory that propagates itself because it would be really cool if it were true, but the usual explanations produce false predictions.)