Given a question as follows.
Find the greatest $x$ that divides 14, 19, 25, 52 and leaves remainders 4, 1, 5 and 2, respectively.
For me this question does not make sense. Because the $\text{HCF}$ of $14-4$, $19-1$, $25-5$, and $52-2$ is $\text{HCF}(10,18,20,50)=2$.
Here if $x=2$ then it divides 14 without remainder. But the question said its remainder is 4. Or I am wrong?
Question
How to properly explain that this question does not make sense?