1. Among the positive integers $n$ less than 100, the possible values of $n$ that allow the fraction $\frac{1}{(3 n+32)(4 n+1)}$ to be expressed as a finite decimal in base 10 are $\qquad$
1.6 or 31.
From the problem, we know that $(3 n+32)(4 n+1)$ can only contain the prime factors 2 or 5. $4 n+1$ is odd, and $5 \leqslant 4 n+1<401$, so $4 n+1=5$ or 25 or 125. Therefore, $n=1$ or 6 or 31. When $n=1$, $3 n+32=35=5 \times 7$, which does not meet the condition. It is easy to verify that $n=6$ or 31 satisfies the condition.