Calculating in floating sexagesimal place value notation, 4000 years ago

Summary form only given, as follows. The full paper was not made available as part of this conference proceedings. By the end of the third millennium BCE in Mesopotamia an innovation of major significance for the history of mathematics occurred: the sexagesimal place value notation. A sophisticated mathematical culture was subsequently developed by masters attached to the scribal schools that flourished in Iraq, Iran and Syria during the first centuries of the second millenium BCE. The best known aspect of this mathematical culture is the art of solving quadratic problems. The numerical algorithms exploiting the properties of base 60 and the floating notation are less known. This paper presents some of these algorithms, especially those based on factorization methods.