The total number of positive integral solutions (x, y, z) of x y z=24 is

Step-by-step solution

x y z=24=2^3 3 Let x=2^ x₁ 3^ y₁ , y=2^ x₂ 3^ y₂ and z=2^ x₃ 3^ y₃ x₁+x₂+x₃=3 and y₁+y₂+y₃=1 Number of non-negative integral solution = 3+3-1 3-1 = ^5 C₂=10 Number of non-negative integral solution = 1+3-1 3-1 = ^3 C₂=3 The total number of positive integral 10 3=30