The total number of positive integral solutions for `(x, y, z)` such that `xyz = 24` is

Options

A. 36
B. 90
C. 120
D. none of these

Explanation

We have,
`24=2xx3xx4`
`=2xx2xx6`
`=1xx6xx4`
`=1xx3xx8`
`=1xx2xx12`
`=1xx1xx24`
Hence, the total number of positive integral solutions of xyz=24 is
`3!+(3!)/(2!)+3!+3!+(3!)/(2!)=6+3+6+6+6+3=30`