Find the number of positive integral solutions of `x y z=21600.`

Find the number of positive integral solutions of abc=45.

The number of positive integral solutions of abcd=210, is

Find the number of positive integral solutions of the equation x+y+z=12.

Find the total number of positive integral solutions for (x,y,z) such that xyz=24 Also find out the total number of integral solutions.

Find the number of positive integral solutions of the inequality 3x+y+z<=30.

Find the number of non-negative integral solutions of x+y+z+w<=20.

Find the number of positive integral solutions of tan ^(-1)x+cot^(-1)y=tan^(-1)3