Let x= the value of divisor, x>8. Then for some integers m and n
3187=mx+8,3319=nx+8
3319−3187=(n−m)x
(n−m)x=132
132=2⋅2⋅3⋅11The list of all positive divisors is as follows: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Since >8, then the smallest possible value of the divisor is 11.
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