<p>This research work presents a complete classification of Friedmann–Robertson–Walker (FLRW) spacetimes based on Noether symmetries. Various classes are analyzed for flat, open, and closed universe models. According to this classification we have various forms of cosmic scale factor <i>b</i>(<i>t</i>). Different sets of Noether symmetries are reported for different classes of FLRW universe. We obtained different classes of the said spacetime along with their Noether symmetries and the corresponding conservation laws. The main objective of this research is to find all possible forms of the scale factor <i>b</i>(<i>t</i>) and discuss their physical significance.</p>