Question:
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
(d) 1001
Solution:
The correct answer is option
(d) 1001
Explanation:
From the given question, the number should be of the form abcabc
So the general form of abcabc is 1000000a+100000b+1000c+100a+10b+c
Now, abcabc = is 1000000a+100000b+1000c+100a+10b+c
By simplifying the above expression, we will get
abcabc = 1001(100a+10b+c)
Hence, the six digit number should be divisible by 1001.