The greatest four-digit number divisible by 6 is 9996.
Here's how we arrive at that answer:
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The largest four-digit number is 9999.
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To determine if it is divisible by 6, we can check if it's divisible by both 2 and 3 (since 6 = 2 x 3).
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A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). 9999 ends in 9, so it is not divisible by 2.
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A number is divisible by 3 if the sum of its digits is divisible by 3. For 9999, the sum of the digits is 9+9+9+9 = 36, which is divisible by 3. However, since it's not divisible by 2, it's not divisible by 6.
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To find the largest four-digit number divisible by 6, we can start subtracting 1 from 9999 until we find a number divisible by 6.
- 9998 is even (divisible by 2), but 9+9+9+8 = 35, which is not divisible by 3.
- 9997 is not even, so not divisible by 2.
- 9996 is even (divisible by 2), and 9+9+9+6 = 33, which is divisible by 3.
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Therefore, 9996 is divisible by both 2 and 3, and hence by 6.
