10. If 2017,1029 and 725 leave a remainder of $\mathrm{r}$ when divided by $\mathrm{d}$, then the maximum value of $\mathrm{d}-\mathrm{r}$ is
Analysis: Remainder and Congruence.
(1) 2017-1029=988, 1029-725=304, since 2017,1029 and 725 have the same remainder \( r \) when divided by \( d \), so \( d \mid 988 \), \( d \mid 304 \), \( d \) is a common divisor of 988 and 304.
(2) \( 988=2^{2} \times 13 \times 19, 304=2^{4} \times 19 \), so \( d \) can be \( 2, 4, 19, 38, 76 \).
(3) Upon inspection, the remainders of 2017, 1029, and 725 when divided by 76 are 41, 41, 41; the remainders of 2017, 1029, and 725 when divided by 38 are 3, 3, 3; the remainders of 2017, 1029, and 725 when divided by 2 are all 1; the remainders of 2017, 1029, and 725 when divided by 4 are all 1; the remainders of 2017, 1029, and 725 when divided by 19 are 3, 3, 3.
(4) The maximum value of \( d - r \) is 35.