105. Repeating quartet of digits. If we multiply 64253 by 365, we get 23452345, where the first four digits repeat.

What is the largest number by which 365 must be multiplied to obtain a similar product containing eight digits, the first four of which repeat?
105. Multiplying 273863 by 365, we get 99959 995. Notice that any eight-digit number, where the first four digits are repeated, is divisible by 73 (and by 137). Moreover, if such a number ends in 5 or 0, it is also divisible by 365 (or by 50005). Knowing these facts, we can immediately write down the answer.