# A Unique 10-digit Number

**Number Theory**Level 3

There exists a unique 10-digit number \(\overline{abcdefghij}\) which contains each of the digits 0, 1, 2, \(\dots\), 9 exactly once, such that for each \(k\), \(1 \le k \le 10\), the number formed by the first \(k\) digits of \(\overline{abcdefghij}\) is divisible by \(k\). For example, for \(k = 4\), the number \(\overline{abcd}\) is divisible by 4.

Find the three-digit number \(\overline{abc}\).