combiphobia..!!

24 has the divisors $\left\{ 1, 2, 3, 4, 6, 8, 12, 24 \right\}$

Let me use Python to enumerate the possibilities. (Otherwise it would be beyond my old brain.)

>>> from sympy import divisors

>>> d=divisors (24)

>>> count=0

>>> for x in d :

... for y in d :

... for z in d :

... if x y z==24:

... count+=1

...

>>> count

30

These are all the positive integer possibilities. One can assign minus signs to the elements of each triples in three ways. Hence, the total number of possibilities is 120.