1. Given the sum of $n$ positive integers is 2017. Then the maximum value of the product of these $n$ positive integers is $\qquad$ .
$$
\text { II. } 1.2^{2} \times 3^{671} \text {. }
$$

Since when $1 \times m4$, $2(m-2)>2+(m-2)$.
Therefore, when a $m$ is replaced by a 2 and a $m-2$, the product increases.

Also, $4+4=2+3+3$, but $4 \times 4<2 \times 3 \times 3$, so the $n$ numbers can only be 2 and 3, where the number of 2s does not exceed 2, and $2017=3 \times 671+2 \times 2$.

Thus, the maximum value of the product of these $n$ positive integers is $2^{2} \times 3^{671}$.