Find the number nearest to $34581$ which is divisible by $9$.

A number is divisible by 9 if the sum of its digits is divisible by 9.Let's check the sum of the digits of the given number $34581$:
$$\text{Sum of digits}=3+4+5+8+1=21$$
Since $21$ is not divisible by 9, the number $34581$ itself is not divisible by 9.The closest multiples of 9 to $21$ are $18$ and $27$.To get a sum of $18$, we subtract: $21-18=3$. So, $34581-3=34578$.To get a sum of $27$, we add: $27-21=6$. So, $34581+6=34587$.Let's compare the distances to $34581$:Distance to $34578$ is $|34581-34578|=3$ Distance to $34587$ is $|34581-34587|=6$ Since $3$ is smaller than $6$, the nearest number divisible by 9 is $34578$.