Question:
The integers 34,041 and 32,506 when divided by a three-digit integer $n$ leave the same remainder. What is $n$?
The integers 34,041 and 32,506 when divided by a three-digit integer $n$ leave the same remainder. What is $n$?
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“Same remainder” $\Rightarrow$ divisor must divide the difference of the numbers.
Updated On: Mar 24, 2026
- 289
- 367
- 453
- 307
Show Solution
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The Correct Option is D
Solution and Explanation
If two numbers leave the same remainder when divided by $n$, then their difference is divisible by $n$.
Difference:
\[
34041 - 32506 = 1535
\]
We need a three-digit divisor of 1535.
Factorising:
\[
1535 \div 5 = 307
\]
Since $307$ is prime and three-digit, $n = 307$.
\[
\boxed{n = 307}
\]
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