6. (3 points) It is known that when 2008 is divided by some natural numbers, the remainder is always 10. There are $\qquad$ such natural numbers.

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6. (3 points) It is known that when 2008 is divided by some natural numbers, the remainder is always 10. There are $\qquad$ 11 such natural numbers.

【Solution】Solution: $2008-10=1998$ must be divisible by these numbers, and these numbers must be greater than 10, $1998=2 \times 3 \times 3 \times 3 \times 37$.
The total number of factors of 1998 is: $(1+1) \times(3+1) \times(1+1)=16$.
Among them, those less than 10 are: $1,2,3,6,9$.
Therefore, the factors greater than 10 are $16-5=11$.
That is, there are 11 such natural numbers.
Hence, the answer is: 11.