A whole number has exactly 6 positive factors. One of its factors is 16 . Which of the following could this number be?
(A) 16
(B) 32
(C) 6
(D) 49
(E) 48
Let the unknown whole number be $n$.

Since 16 is a factor of $n$, then each positive factor of 16 is also a factor of $n$.

That is, the positive factors of $n$ include 1, 2, 4, 8, 16, and $n$.

Since 16 is a factor of $n$, then $n$ is a positive multiple of 16 .

The smallest whole number multiple of 16 is 16 .

However, if $n=16$, then $n$ has exactly 5 positive factors, namely $1,2,4,8$, and 16 .

The next smallest whole number multiple of 16 is 32 .

If $n=32$, then $n$ has exactly 6 positive factors, namely $1,2,4,8,16$, and 32 , as required.

ANSWER: (B)