8. Let $a, b$ be two positive integers, their least common multiple is $2^{5} \cdot 3^{3} \cdot 7^{2} \cdot 11$, then the number of ordered pairs of positive integers $(a, b)$ is $\qquad$.


8. 1155 Explanation: Let $a=2^{\alpha_{1}} \cdot 3^{\alpha_{2}} \cdot 7^{\alpha_{3}} \cdot 11^{\alpha_{4}}, b=2^{\beta_{1}} \cdot 3^{\beta_{2}} \cdot 7^{\beta_{3}} \cdot 11^{\beta_{4}}$, then we have $\left\{\alpha_{1}, \beta_{1}\right\}_{\max }=5,\left\{\alpha_{2}, \beta_{2}\right\}_{\max }=3,\left\{\alpha_{3}, \beta_{3}\right\}_{\max }=2,\left\{\alpha_{4}, \beta_{4}\right\}_{\max }=1$. Therefore, the number of ordered positive integer pairs $(a, b)$ is $(2 \times 5+1)(2 \times 3+1)(2 \times 2+1)(2 \times 1+1)=1155$.