The smallest five-digit number divisible by 3 is 10002.
To understand why this is the case, let's break it down:
- Understanding Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Smallest Five-Digit Number: The smallest five-digit number is 10000.
- Checking Divisibility: The sum of the digits of 10000 is 1 + 0 + 0 + 0 + 0 = 1, which is not divisible by 3.
- Finding the Next Divisible Number: To find the next number divisible by 3, we keep incrementing the number and re-checking. The sum of the digits of 10001 is 1 + 0 + 0 + 0 + 1 = 2, also not divisible by 3.
- The Answer: The sum of the digits of 10002 is 1 + 0 + 0 + 0 + 2 = 3, which is divisible by 3. Therefore, 10002 is the smallest five-digit number that meets the criteria.
As highlighted in the reference, the smallest positive 5-digit number exactly divisible by 3 is indeed 10002.
