Minimum Number of Divisors

Number Theory Level pending

What is the minimum number of divisors for the 8-digit number \( \overline{abbaabba} \), where \(a\) and \( b\) are integers from 1 to 9?

Details and assumptions

\( \overline{abc}\) means \( 100a + 10b + 1c\), as opposed to \( a \times b \times c\). As an explicit example, for \(a=2, b=3, c=4\), \(\overline{abc} = 234\) and not \( 2 \times 3 \times 4 = 24\).

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