MCQ
A six-digit number is formed by repeating a three-digit number. For example $256256, 678678,$ etc. Any number of this form is divisible by
- A$7$ only
- B$11$ only
- C$13$ only
- ✓$1001$
✓
Answer
Correct option: D.
$1001$
Let the six-digit number be $abcabc,$ then
$= 100000 × a + 10000b + 1000c + 100a + 10b + c$
$= a(100000 + 100) + b(10000 + 10) + c(1000 + 1)$
$= a(100100) + b(10010) + c(1001) = 1001(a × 100 + b × 10 + c)$
Hence, it is divisible by $1001$
$= 100000 × a + 10000b + 1000c + 100a + 10b + c$
$= a(100000 + 100) + b(10000 + 10) + c(1000 + 1)$
$= a(100100) + b(10010) + c(1001) = 1001(a × 100 + b × 10 + c)$
Hence, it is divisible by $1001$
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