Three readings. As a noun 数 ('number, figure') it carries the fourth tone: 数学, 数字, 次数. As a verb meaning 'to count' it switches to 数 (third tone). A rare literary reading 数 ('frequently') survives in 数见不鲜.
usage
Before a measure word or number-amount, 数 also means 'several / a few': 数天 (a few days), 数百 (several hundred), 数以万计 (numbering in the tens of thousands). Same fourth-tone reading as the noun sense.
Strike radical on the right (the contracted form of 攴) - the indexing radical. Reflects the original act of tallying or beating out a count, perhaps with a stick on a tally board. Productive in action verbs of authority and process: 教 (teach), 收 (gather), 改 (change), 政 (govern).
Left 娄 supplies the sound - lóu → shù shows heavy Old Chinese drift, but the whole phonetic series (楼 building, 搂 embrace, 缕 thread) shares the same root. Simplified from traditional 數 with the same 婁/娄 phonetic, just streamlined.
