The seventy-two are conventionally arranged in nine groups of eight, each group assigned to a choir of angels, to a sephirah and to a governing archangel. The arithmetic is exact and the structure is elegant. Its parts come from three different places.
The nine choirs are from The Celestial Hierarchy, a Greek Christian treatise written around the year 500 under the name of Dionysius the Areopagite, the Athenian convert mentioned in Acts. The attribution is false and has been known to be false since the Renaissance, Isaac Casaubon's critical work of 1614 is part of the same movement that unmasked it, but the text is a genuine and important piece of late antique Christian Neoplatonism. It sets out three triads: Seraphim, Cherubim and Thrones; Dominions, Virtues and Powers; Principalities, Archangels and Angels.
The sephiroth are the ten emanations of Kabbalistic theosophy, systematised in the Zohar and in the literature around it. There are ten of them, not nine, so the mapping onto the choirs requires an adjustment, usually by treating Kether and Chokmah differently or by omitting Malkuth from the scheme.
The archangels are a further layer, drawn from Jewish angelological sources of varying date, in which Metatron, Raziel, Tzaphkiel, Tzadkiel, Khamael, Michael, Haniel, Raphael and Gabriel are assigned to the sephiroth.
Overlaying the three and dividing seventy-two by nine to get eight is Christian Kabbalah at work. It is a genuine tradition with a real history, and its result is coherent. But no one before the sixteenth century could have stated it, because two of its three components had never been brought into contact before then.