The specific pairing of thirty three, thirty three and thirty four recitations, known as the tasbih of Fatima, is anchored in a hadith recorded in the major Sunni collections describing how the Prophet, unable to give his daughter Fatima a household servant she had asked for, taught her this formula instead as something of greater lasting benefit, said upon retiring for the night. That narrative is what fixes the specific counts practiced today, rather than the Quran itself, which supplies the vocabulary of glorification generally without specifying numbers.
How the count should be kept has its own minor history of disagreement. The earliest and least disputed method is counting on the joints and tips of the fingers of the right hand, a practice attributed to the Prophet in hadith and still preferred by some scholars on that authority alone. The tasbih, a string of prayer beads, is a later tool for the same counting task, and its permissibility was debated by early jurists precisely because it lacked the same direct prophetic attribution as finger counting, with some conservative opinion treating beads as an unnecessary innovation and more accommodating opinion treating them as a permissible aid to an act whose substance the Prophet himself endorsed regardless of the counting method used. Both positions persist today, and the continued use of the word tasbih for the beads themselves, rather than only for the recitation, reflects how thoroughly the tool and the formula have merged in ordinary usage even where jurists keep them conceptually separate.