Task 3. Determine the smallest four-digit number that is divisible by 9, if the product of its digits is equal to 180.
Solution. From $180=1 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$ it follows that the digits which can give a product of 180 can be: $1,4,5,9$ or $1,5,6,6$ or $2,2,5,9$ or $3, 3,4,5$ or $2,3,5,6$. However, the number must be divisible by 9, which means the sum of its digits must be divisible by 9. From this, we conclude that the digits of the number can be $1,5,6,6$ or $2,2,5,9$. Since we are looking for the smallest number with the required properties, we conclude that it is the number 1566.