Question:

A three-digit number is selected such that it contains no zeros. Now this three-digit number is written beside itself to form the six-digit number. Its factor is _______.

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When a number is repeated (e.g., abcabc), it's always divisible by 1001, which is \( 7 \times 11 \times 13 \).
Updated On: Jun 12, 2025
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The Correct Option is B

Solution and Explanation

Step 1: Assume a three-digit number \( xyz \). This is written beside itself: \[ xyzxyz = xyz \times 1000 + xyz = xyz \times (1000 + 1) = xyz \times 1001 \] Step 2: Prime factorization of 1001:
\[ 1001 = 7 \times 11 \times 13 \] So, any such number formed by repeating a 3-digit number will always be divisible by 7, 11, and 13. Hence, 11 is definitely a factor.
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