$\large \displaystyle{A=\left\{ 1,2,3,5,6,10,15,30 \right\} }$

For set $A$ , find the number of positive integral solution of $(x,y,z)$ that satisfy the condition $xy z \in a$ .

The answer is 64.

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is there a better way than to observe that all numbers must be powers of 2 and 5 and 3 and their products, from which 1 comes in one way , 2,3,5 in 3 ways each, 6,10,15 in 9 ways each(products of two taken at a time) and 30 in 27 ways (product of all 3) so total 64