The largest four-digit number divisible by 6 is 9996.
To find this, we can start with the largest four-digit number, which is 9999, and work backwards. A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisibility Rule for 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- Divisibility Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
9999 is not divisible by 2 because its last digit is 9 (odd).
Also, 9 + 9 + 9 + 9 = 36, which is divisible by 3, so 9999 is divisible by 3.
Let's try the next smaller number, 9998. This is divisible by 2, but 9 + 9 + 9 + 8 = 35, which is not divisible by 3.
Let's try 9997. This is not divisible by 2, and 9 + 9 + 9 + 7 = 34, which is not divisible by 3.
Finally, let's try 9996. This is divisible by 2 because its last digit is 6 (even). Also, 9 + 9 + 9 + 6 = 33, which is divisible by 3. Therefore, 9996 is divisible by both 2 and 3, and thus divisible by 6.
