# 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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