These types of problems (where you repeat some portion of a number) involve factoring out the "repeated portion" and then examining the other factor.
So, let's say the number you repeat is represented in digits as ABCD. We'd have:
ABCDABCD = 10,000⋅ABCD + 1⋅ABCD = 10,001⋅ABCD
Now, simply note that 10,001 = 73⋅137.