The term 'greatest extent' can be defined by the crossword solutions of UTMOST (6 letters), fullest (7 letters), and LENGTH (6 letters). UTMOST means the highest degree or greatest amount possible, while fullest implies the maximum amount or degree. Lastly, LENGTH refers to the measurement of the longest dimension of an object. Together, these three words describe the greatest extent of something, which is the highest degree or maximum amount of something that can be achieved.