The positive factors of 6 are $1,2,3$, and 6 . There are two perfect squares less than 100 that have exactly five positive factors. What is the sum of these two perfect squares?
(A) 177
(B) 80
(C) 145
(D) 52
(E) 97
A perfect square is a number that can be expressed as the product of two equal integers.

By this definition, 0 is a perfect square since $0 \times 0=0$.

Since the product of 0 and every positive integer is 0 , then every positive integer is a factor of 0 , and so 0 has an infinite number of positive factors.

The next three smallest perfect squares are $1^{2}=1,2^{2}=4$ and $3^{2}=9$.

Each of these has at most three positive factors.

The next largest perfect square is $4^{2}=16$.

The positive factors of 16 are $1,2,4,8$, and 16 , and so 16 is a perfect square that has exactly five positive factors.

The remaining perfect squares that are less than 100 are $25,36,49,64$, and 81 .

Both 25 and 49 each have exactly three positive factors.

The positive factors of 36 are $1,2,3,4,6,9,12,18$, and 36 .

The positive factors of 64 are $1,2,4,8,16,32$, and 64 .

Thus, both 36 and 64 each have more than five positive factors.

Finally, the positive factors of 81 are $1,3,9,27$, and 81 .

The two perfect squares that are less than 100 and that have exactly five positive factors are 16 and 81 , and their sum is $16+81=97$.

ANSWER: (E)