8. (10 points) The integer $n$ has a total of 10 factors. These factors, arranged in ascending order, have the 8th one as $\frac{\mathrm{n}}{3}$. What is the maximum value of the integer $n$? $\qquad$ .
8. (10 points) The integer $n$ has a total of 10 factors. These factors, arranged from smallest to largest, have the 8th one as $\frac{\mathrm{n}}{3}$. What is the maximum value of the integer $n$? $\qquad$ _.

【Analysis】Since the factors of an integer always appear in pairs, the 10 factors must be 1, $\qquad$, 3, $\qquad$, $\qquad$, $\qquad$, $\qquad$, $\frac{n}{3}$, $\qquad$, $n$. We can immediately fill in $1$, $2$, 3, $\qquad$, $\qquad$, $\qquad$, $\qquad$, $\frac{\mathrm{n}}{3}$, $\frac{\mathrm{n}}{2}$, $n$. This means that $n$ must contain the prime factors 2 and 3. Then, using the divisor count theorem, we can solve the problem.

【Solution】According to the analysis, the 10 factors are $1$, $2$, $3$, $\qquad$, $\qquad$, $\qquad$, $\qquad$, $\frac{n}{3}$, $\frac{\mathrm{n}}{2}$, $n$.

According to the divisor count theorem, $10=1 \times(9+1)=(1+1) \times(4+1)$.
Since $n$ contains the prime factors 2 and 3, $n$ should be $2^{1} \times 3^{4}$ or $2^{4} \times 3^{1}$. Among these, $2^{1} \times 3^{4}=162$ is larger. Therefore, the answer is: 162.