Concatenate a 3-digit number with itself (e.g. 835 -> 835835). Divide it by 7.
The remainder will be zero!
Exampple: 235235 / 7 = 33605
Now, divide the quotient by 11. The remainder will be zero!
Exampple: 235235 / 7 = 33605 -> 33605 / 11 = 3055
Again, divide the recent quotient by 13. The remainder will be zero!
Exampple: 235235 / 7 = 33605 -> 33605 / 11 = 3055 -> 3055 / 13 = 235
Where 235 is the original number!
Another example:
Take 743!
Concatenate it with itself: 743743
Divide it by 7: 743743 / 7 = 106249
Divide the quotient by 11: 106249 / 11 = 9659
Divide the recent quotient by 13: 9659 / 13 = 743
Why?
7 * 11 * 13 = 1001
Multiplying 1001 by any 3-digit number will be as concatenating it with itself:
100 * 1001 = 100100
945 * 1001 = 945945
So, any number that is obtained by concatenating a 3-digit number with itself can be divided by 1001 and as 1001 is equal to 7 * 11 * 13, it can be divided by 7, 11, and 13.