What is the six-digit number divisible by 6?

The question is under-specified. There are infinitely many six-digit numbers divisible by 6. To provide a useful answer, we can determine either:

1. The smallest six-digit number divisible by 6: This would be 100002.
2. The largest six-digit number divisible by 6: This would be 999996.

Let's elaborate on how these numbers are found:

Finding the Smallest Six-Digit Number Divisible by 6

1. The smallest six-digit number is 100000.
2. Divide 100000 by 6: 100000 / 6 = 16666.666...
3. Round up to the next whole number: 16667
4. Multiply by 6: 16667 * 6 = 100002.
5. Therefore, the smallest six-digit number divisible by 6 is 100002.

Finding the Largest Six-Digit Number Divisible by 6

1. The largest six-digit number is 999999.
2. Divide 999999 by 6: 999999 / 6 = 166666.5
3. Round down to the previous whole number: 166666
4. Multiply by 6: 166666 * 6 = 999996
5. Therefore, the largest six-digit number divisible by 6 is 999996. This agrees with the reference.

General Considerations for Divisibility by 6

A number is divisible by 6 if and only if it is divisible by both 2 and 3.

• Divisibility by 2: The number must be even (end in 0, 2, 4, 6, or 8).
• Divisibility by 3: The sum of the digits of the number must be divisible by 3.

For example, consider 999996:

• It ends in 6, so it's divisible by 2.
• The sum of its digits is 9+9+9+9+9+6 = 51, which is divisible by 3 (51/3 = 17).
• Therefore, 999996 is divisible by 6.

If the intent of the question was to find a six-digit number divisible by 6, then many answers are valid. For example, 500010 is divisible by 6. If no other constraint is given, 100002 or 999996 can serve as a valid answer with the minimum/maximum as additional information.