Question : Any six-digit number that is formed by repeating a three-digit number, is always divisible by:
Option 1: 111
Option 2: 1001
Option 3: 19
Option 4: 101
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Correct Answer: 1001
Solution :
Let the six-digit number be of the form be 'abcabc'.
The number can be expressed as:
= 100000a + 10000b + 1000c + 100a + 10b + c
= 100100a + 10010b + 1001c
= 1001(100a + 10b + c)
So, 1001 is a factor of 'abcabc' for any values of a, b and c.
Hence, the correct answer is 1001.
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