# Find the greatest $x$ that divides 14, 19, 25, 52 and leaves remainders 4, 1, 5 and 2, respectively

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?

• @LukasKofler: 2 divides 14 without remainder. – Well Harassed Programmer Aug 22 at 14:26
• @MoneyOrientedProgrammer It could: $14 = 5\cdot 2 + 4$. Depending on how your problem author meant "leaves remainder". It's not standard, but it's conceivable. – Arthur Aug 22 at 14:26
• @Arthur So, the question could be rephrased as $14\equiv4\pmod{x}$ and so forth? – saulspatz Aug 22 at 14:30
• You are right $-$ the question makes no sense. – TonyK Aug 22 at 14:32
• The only numbers that divide 14 with a remainder of 4 are 5 and 10. They do not satisfy the other conditions, so there is no solution. – Gabe Aug 22 at 14:58