How sound is the Hadith: "Purity is half of faith, and filth is from Satan"?

The phrase "Cleanliness is part of faith, and filthiness is from Satan" is not a prophetic hadith, but its meaning is sound and supported by many religious texts that call for purity and cleanliness in the body, clothing, and dwelling, such as the Almighty's saying: ﴿And purify your garments﴾ [74:4], and the Prophet's (peace be upon him) saying: "Cleanse these bodies, may Allah cleanse you, for there is no servant who goes to bed in a state of purity except that an angel spends the night with him in his inner garment," and "Cleanse your courtyards, for the Jews do not cleanse their courtyards."