The number of positive integral solutions of ${\mathrm{x}}_1.{\mathrm{x}}_2.{\mathrm{x}}_3=30$ is
 

${\mathrm{x}}_1.{\mathrm{x}}_2.{\mathrm{x}}_3=2\times 3\times 5$

$\mathrm{Let} {\mathrm{x}}_1=2^{a_1}{3}^{b_1}{5}^{c_1},x_2=2^{a_2}{3}^{b_2}{5}^{c_2},x_3=2^{a_3}{3}^{b_3}{5}^{c_3}$

$\therefore x_1{x}_2{x}_3=2^{a_1+a_2+a_3}{3}^{b_1+b_2+b_3}{5}^{c_1+c_2+c_3}$

$\Rightarrow a_1+a_2+a_3=1,b_1+b_2+b_3=1,c_1+c_2+c_3=1$

Number of solutions=${\left({ }^{\left(1+3-1\right)}{C}_{3-1}\right)}^3={\left({ }^3{C}_2\right)}^3=27$