6. (10 points) The sum of 13 different natural numbers is 996, and the sum of the digits of these numbers are all equal. Find these 13 numbers.

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【Analysis】The remainder when the sum of the digits of several addends is divided by 9 is the same as the remainder when the sum of these addends is divided by 9; 996 divided by 9 leaves a remainder of 6, so the sum of the digits of these 13 numbers divided by 9 also leaves a remainder of 6. Since the sum of the digits of these 13 numbers is equal, the sum of the digits of these 13 numbers could be $6, 15, 24$; further calculations can be made accordingly.

【Solution】Solution: $996 \div 9=110 \cdots 6$,
So the sum of the digits of these 13 numbers divided by 9 also leaves a remainder of 6,
Since the sum of the digits of these 13 numbers is equal, the sum of the digits of these 13 numbers could be $6, 15, 24$; the smallest 13 numbers with a digit sum of 6 are $6, 15, 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150$; the sum of these 13 numbers is exactly 996. Therefore, these 13 numbers are: $6, 15, 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150$.