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 _______.

• A. 5
• B. 11
• C. 4
• D. 44

Hint:

When a number is repeated (e.g., abcabc), it's always divisible by 1001, which is \( 7 \times 11 \times 13 \).

Answer 1

The Correct Option is B

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.