In order for a three-digit integer to be divisible by 13, the number formed by its last 2 digits must be divisible, while the first digit minus 1 times 10 must make a multiple of 13.
To find a 3-digit multiple of 13, we look for such numbers that go from 1 to 1000. To find the highest 3-digit number that is a multiple of 13, subtract 13 until you get 3-digit numbers. Since 1000 divided by 13 leaves a remainder of 3, the greatest 3-digit number divisible by 13 is $\boxed{988}$.
All of the digits of a three-digit integer are distinct and non-zero. Furthermore, the three-digit integer is divisible by 13. Find the largest three-digit integer that has these properties.
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