8. Let the rational number $r=\frac{p}{q} \in(0,1)$, where $p, q$ are coprime positive integers, and $pq$ divides 3600. The number of such rational numbers $r$ is $\qquad$ .
$$
3600=2^{4} \times 3^{2} \times 5^{2}, p q \mid 2^{4} \times 3^{2} \times 5^{2},(p, q)=1 \text { and } q>p \text {. }
$$
When $p=1$, $q$ has 44 values; when $p=2$, $q$ has 8 values; when $p=4$, $q$ has 7 values; when $p=8$, $q$ has 6 values; when $p=16$, $q$ has 4 values; when $p=3$, $q$ has 13 values; when $p=9$, $q$ has 10 values; when $p=5$, $q$ has 11 values; when $p=25$, $q$ has 4 values; when $p=6$, $q$ has 1 value; when $p=12$, $q$ has 1 value; when $p=24$, $q$ has 1 value; when $p=18$, $q$ has 1 value; when $p=15$, $q$ has 1 value.
In summary, the number of rational numbers $r$ is 112.