When 7897, 8110 and 8536 are divided by the greatest number x, then the remainder in each case is the same. The sum of the digits of x is:
6
If three numbers leave the same remainder when divided by \(x\), then \(x\) divides every pairwise difference. The greatest such \(x\) is the HCF of those differences.
\[8110-7897=213,\quad 8536-8110=426\]
\[\gcd(213,426)=213\quad(\text{since }426=2\times 213)\]
So \(x=213\) and the digit sum is \(2+1+3=\mathbf{6}\).
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