1. Find the smallest positive integer $n$, such that $n$ is divisible by 3 and the product of its digits is 882.
1. The required integer $n$ is 13677.

Since $882=2 \times 3^{2} \times 7^{2}$, the digits of $n$ greater than 1 could be
$(2,3,3,7,7) 、(2,7,7,9)$ or $(3,6,7,7)$.
Noting that $n$ is divisible by 3.
Thus, the smallest values of $n$ in these three cases are $1123377 、 112779$ and 13677, respectively.
In conclusion, the required integer $n$ is 13677.