A string of beads pulled through the fingers to count repetitions appears across most of the praying world, and the convergence is worth examining rather than assuming.
The mala in Hindu and Buddhist use most often has 108 beads, a number given several rationales after the fact, with a larger head bead that is not counted and is not crossed: the practitioner reverses direction at it instead. Materials carry meaning. Rudraksha seeds are used in Shaiva practice, tulsi wood in Vaishnava, bodhi seed or bone in Buddhist practice, and the choice announces an affiliation.
The Muslim tasbih commonly has ninety-nine beads, or thirty-three told three times, matching the standard formula recited after prayer. The Catholic rosary in ordinary use has five decades on a loop, itself descended from the medieval practice of substituting a hundred and fifty prayers for the hundred and fifty psalms. Orthodox Christians use a knotted wool cord, often of a hundred knots, tied in a pattern that is given its own symbolic explanation.
Whether these are historically connected is genuinely open, and it is worth resisting a confident answer. Prayer beads are attested in India well before they appear in Christian Europe, and a route of transmission through the Middle East is plausible and has never been demonstrated. Independent invention is equally plausible, because the problem being solved is the same everywhere and there are not many ways to solve it: how to keep an accurate count of a repetition while the mind is deliberately not engaged in counting. The hand does the arithmetic so the attention does not have to. That is a good enough reason for four traditions to arrive at the same object without meeting.