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Question

What is the smallest number with exactly five factors?



A

32

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B

36

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C

16

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D

20

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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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