Question

What is the smallest number with exactly five factors?

• A. 32
• B. 36
• C. 16
• D. 20

Answer 1

The correct option is C

16

Note the following:
$16=2\times 2\times 2\times 2$, and hence has exactly $4+1=5$ factors.
$32=2\times 2\times 2\times 2\times 2$, and hence has exactly $5+1=6$ factors.
$36=2\times 2\times 3\times 3$, and hence has exactly $(2+1)(2+1)=9$ factors.
$20=2\times 2\times 5$, and hence has exactly $(2+1)(1+1)=6$ factors.

Hence, 16 is the number with exactly 5 factors.