A two-digit number has repeated digits. The number of such numbers having exactly $$4$$ positive divisors is

Correct Answer: 4

Solution

The repeated-digit numbers are $$11,22,33,44,55,66,77,88,99$$. Exactly four divisors occur for $$22=2 \times 11$$, $$33=3 \times 11$$, $$55=5 \times 11$$ and $$77=7 \times 11$$. Therefore, the count is $$4$$.

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