Question

If we have the same remainder (non-zero) when dividing the numbers 863 and 814 by a number $x$, then the value of $x$ is

• A. 3
• B. 5
• C. 7
• D. 9

Hint:

Same remainder problems reduce to checking divisors of the difference.

Answer 1

The Correct Option is C

To find the value of \(x\) such that both 863 and 814 give the same non-zero remainder when divided by \(x\), we use the property that the difference between the two numbers (863 and 814) must be divisible by \(x\).

1. Find the difference between the two numbers: \(863 - 814 = 49\).
2. We need to find an \(x\) that divides 49 exactly, meaning \(x\) must be a factor of 49.
3. The factors of 49 are 1, 7, and 49.
4. We are looking for a non-zero remainder; hence, \(x\) cannot be 49 as it would leave zero remainder.
5. Thus, \(x\) must be 7, as it is the only factor of 49 other than 1 and 49 itself which meets the condition of leaving a non-zero remainder for both numbers.

Upon dividing 863 and 814 by 7, both will give the same remainder, and thus the value of \(x\) is 7.