The smallest 4-digit odd number divisible by 3 is 1005.
Let's break down how to find this answer:
According to a provided reference, 1002 is the smallest 4-digit number divisible by 3. However, 1002 is an even number, and the question asks for the smallest odd number.
To find the next multiple of 3, we can consider increasing 1002 by 1 each time to determine when we get an odd number.
- 1002 is divisible by 3 (as provided in the reference)
- 1003 is not divisible by 3 (sum of digits is 4)
- 1004 is not divisible by 3 (sum of digits is 5)
- 1005 is divisible by 3 (sum of digits is 6) and it is an odd number.
Therefore, the smallest 4-digit odd number divisible by 3 is 1005.
Explanation
- Four-Digit Number: A four-digit number is any number between 1000 and 9999.
- Odd Number: An odd number is a whole number that cannot be divided evenly by 2. It always ends with the digits 1, 3, 5, 7, or 9.
- Divisible by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Steps to Find the Answer
- Start with the smallest 4-digit number: The smallest four-digit number is 1000.
- Check for divisibility by 3: 1000 is not divisible by 3 (sum of digits is 1).
- Increment and check: We need to find the smallest number greater than 1000 that is both odd and divisible by 3.
- Iterate: Checking the first few numbers greater than 1000, we find that 1002 is divisible by 3 (but it is even). 1003 and 1004 are not divisible by 3. 1005 is the first number meeting all the criteria.
Summary
| Number | Divisible by 3? | Odd? |
|---|---|---|
| 1000 | No | No |
| 1001 | No | Yes |
| 1002 | Yes | No |
| 1003 | No | Yes |
| 1004 | No | No |
| 1005 | Yes | Yes |
