What is the smallest four-digit number that is divisible by $33$?
To find the smallest four-digit number that is divisible by $33$, I need to find the first multiple of $33$ that is greater than or equal to $1000$. I can start by dividing $1000$ by $33$ and see what the quotient and remainder are. Using long division, I get $1000 = 33 \times 30 + 10$, so the quotient is $30$ and the remainder is $10$. This means that $1000$ is not divisible by $33$, but $33 \times 30 = 990$ is the largest three-digit multiple of $33$. To get the next multiple of $33$, I need to add $33$ to $990$. This gives me $990 + 33 = 1023$, which is the smallest four-digit number that is divisible by $33$.

