Calculate the differences

To find the divisor that leaves the same remainder, we find the differences between the numbers: $95 - 57 = 38$ and $211 - 95 = 116$ and $211 - 57 = 154$.

$95 - 57 = 38, \quad 211 - 95 = 116, \quad 211 - 57 = 154$

Find the HCF of the differences

We need the Highest Common Factor (HCF) of 38, 116, and 154.

$\text{HCF}(38, 116, 154)$

Perform prime factorization

Factorize the differences: $38 = 2 \times 19$, $116 = 2^2 \times 29$, $154 = 2 \times 7 \times 11$. Re-checking the differences: the HCF of 38, 116, 154 is indeed 2.

$38 = 2 \times 19, \quad 116 = 2 \times 58 = 2 \times 2 \times 29, \quad 154 = 2 \times 77 = 2 \times 7 \times 11$

Conclusion

The only common factor shared by 38, 116, and 154 is 2. Thus, the greatest number is 2.

$\text{HCF} = 2$