If a three digit positive integers ‘abc’ has 3 positive factors, how

The numbers that have 3 positive factors are those that are a square of a prime. For example, 9 = 3^2 has three factors: 1, 3 and 9. Since here, abc has 3 factors, abc must be a square of a prime, i.e., abc = p^2 where p is a prime (note: The smallest value of p is 11 and the largest value of p is 31).

Since abcabc = abc x 1,001 and 1,001 = 7 x 11 x 13. If abc is neither 11^2 or 13^2, then abcabc = p^2 x 7^1 x 11^1 x 13^1 has (2 + 1)(1 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 x 2 = 24 factors. If abc is 11^2, then abcabc = 11^2 x 7^1 x 11^1 x 13^1 = 7^1 x 11^3 x 13^1 has 2 x 4 x 2 = 16 factors. If abc is 13^2, then, like abc = 11^2, abcabc will also have 16 factors. Therefore, abcabc has either 16 or 24 factors.

Answer: E