7, 13, and 37 will always divide numbers such as 151515, 474747, 868686
Forming a number by "repeating a two digit number three times" is the equivalent of "multiplying a two digit number by 10101". And, as @achuille-hui said, $10101 = 3 \times 7 \times 17 \times 37$. So, any number in your form will be a multiple of 3, 7, 17 and 37.