What is the ruling on using prayer beads (tasbih) for the remembrance of Allah, and is ritual purity (tahara) required for them?

There is no religious impediment to using prayer beads (misbaha) for tasbeeh (glorification of God). However, it is better to perform tasbeeh using the fingertips, based on the Prophet Muhammad's (peace be upon him) saying: "Hold fast to tasbeeh, tahlil (saying 'La Ilaha Illa Allah'), and taqdees (sanctification). Do not be heedless, lest you forget mercy. Count with your fingertips, for they will be questioned and made to speak." Purity (tahara) is not required to use them.