The number of positive integral solution of $\mathrm{abc}=30 \mathrm{is}$

We have : $30=2 \times 3 \times 5 .$ So, 2 can be assigned to either a or b or ci.e. 2 can be assigned in 3 ways. Similarly, each of 3 and 5 can be assigned in 3 ways. Thus, the number of solutions is $3 \times 3 \times 3=27$