The smallest 6-digit number divisible by 9 is 100008.
To determine this, consider the following:
- The smallest 6-digit number: The smallest 6-digit number is 100000.
- Divisibility Rule of 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- Checking 100000: The sum of the digits of 100000 is 1 (1 + 0 + 0 + 0 + 0 + 0 = 1), which is not divisible by 9.
- Finding the Next Divisible Number: We need to find the smallest number to add to 100000 to make the sum of its digits divisible by 9. Since the current sum is 1, we need to add 8 to make the sum 9. Therefore, we add 8 to 100000.
- The Solution: 100000 + 8 = 100008. The sum of the digits of 100008 is 9 (1 + 0 + 0 + 0 + 0 + 8 = 9), which is divisible by 9.
Therefore, 100008 is the smallest 6-digit number that is divisible by 9.
