Find the missing number

You are given a 52 digit number of the form
1111111...(25 times) [?] 1111.......(26 times)
Find the missing number '?' such that the resultant 52 digit number is divisible by 13.

Approach:
Lets assume 13 * X = 1111111...(25 times) [?] 1111.......(26 times)
The key to find the missing number is to find the X
What need should be the units place of X, it can be none another than 7 (7*13 = 91)
Now moving on to tens place of X, we again require a 1 at tens place at the output
so X has the tens place as 4, left as an exercise to the reader.
I similar fashion you can construct 13* 8547 = 00111111
Now we can create a sequence of 24 1's
13 * 008547008547008547008547 = 1111(24 times)
Now the problem reduces to finding a number such that
13 * Y = 1?11 (Since we 24 1's on the left and 24 1's on the right)
Y = 147 and ? = 9
Hence the missing number is 9