A Q-factorial variety is a normal variety on which every Weil divisor has a positive integer multiple that is a Cartier divisor. The multiple can depend on the Weil divisor. A smooth algebraic variety is Q-factorial because every Weil divisor is already a Cartier divisor (Kollár and Mori 1998).
Q-factoriality allows rational pullbacks and intersection numbers for all Weil divisors. It is a standard hypothesis for the classical minimal model program and Mori fiber space construction.
