Question

# What is the smallest number with exactly five factors?

A

32

B

36

C

16

D

20

Solution

## The correct option is C 16 Note the following: 16=2×2×2×2, and hence has exactly 4+1=5 factors. 32=2×2×2×2×2, and hence has exactly 5+1=6 factors. 36=2×2×3×3, and hence has exactly (2+1)(2+1)=9 factors. 20=2×2×5, and hence has exactly (2+1)(1+1)=6 factors.  Hence, 16 is the number with exactly 5 factors. Mathematics

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