Which number has only two factors 12, 14, 15, 17

17

Step-by-step explanation:

17 is prime, so has only 1 and itself as (positive integer) divisors.

12 has positive divisors 1, 2, 3, 4, 6, 12

14 has positive divisors 1, 2, 7, 14

15 has positive divisors 1, 3, 5, 15

___

Comment on "factors"

Sometimes, we make a distinction between (prime) factors and divisors. A factor is often considered to be a prime number that is a divisor, so 1 is not included. (Here, that would mean 14 and 15 have two factors, but 17 does not.) A divisor is considered to be any integer that gives the number when multiplied by another integer. When factoring polynomials, we often also include negative integers among the divisors of the numbers we're concerned with.

Answer: 17