jmc

Since the integer ends in $0$, it is divisible by $2$ and $5$. Because the sum of its digits is divisible by $3$, the number is divisible by $3$, and we know that a number divisible by both $2$ and $3$ is also divisible by $6$. If the number is $30$, however, then it is not divisible by $4$, $8$, or $9$. So exactly $\boxed{4}$ of the numbers in the original problem statement must divide it.