Hey, can someone help me through this GMAT Number Properties question?

Question

How many integers between 1 and 16, inclusive, have exactly 3 different positive integer factors? (Note: 6 is NOT such an integer because 6 has 4 different positive integer factors: 1, 2, 3, and 6.) 
A. 1 
B. 2 
C. 3
D. 4 
E. 6

Aarushi S · Accepted Answer

The only numbers with exactly 3 positive divisors are perfect squares of prime numbers. Why? A number has exactly three divisors only when its prime factorization is in the form of p2p^2p2, where p is a prime. That&rsquo;s because the total number of divisors is found using the exponents in the factorization. For p2p^2p2, the divisors are: 1, p, and p2p^2p2.
Between 1 and 16, the primes are: 2, 3, 5, their squares are: 4, 9, 25. Only 4 and 9 fall in the given range. So just 4 and 9 qualify, each with exactly 3 divisors. Final answer is 2, so choice B.
One easy trap here is to overcheck factors manually. Knowing the rule about prime squares saves a ton of time in similar GMAT questions.

kritika K · Answer

This one&rsquo;s easier once the pattern clicks &mdash; only perfect squares of primes have exactly 3 positive factors.

Prime numbers alone have just 2 factors: 1 and itself.
Square them, and you add one more factor &mdash; the square itself.
That gives exactly 3: 1, the prime, and its square.
From 1 to 16, only 4 (2&sup2;) and 9 (3&sup2;) meet the condition.
25 (5&sup2;) is too large to count.

Every other number either has too few or too many divisors.  So only 4 and 9 qualify. Final answer is 2, which is option B.  A good trick to lock is in if you ever see &ldquo;exactly 3 divisors,&rdquo; think prime squared.