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pushpitkc
How many integers less than 200 will have only 3 factors?

A. 2
B. 4
C. 6
D. 9
E. 12

Self-made


Only the square of the prime has 3 factors. Computation can be done as follows:

\(2^2\) = 4
\(3^2\)= 9
\(5^2\) = 25
\(7^2\) =49
\(11^2\) =121
\(13^2\) =169

these the only squared primes below 200. Thus we have 6 integers below 200.

The best answer is C.
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pushpitkc
How many integers less than 200 will have only 3 factors?

A. 2
B. 4
C. 6
D. 9
E. 12

Self-made

Not sure what I am missing here, but why are we only considering prime numbers in the solution?
Why can't one solution be 1 x 3 x 5 or anything like that?
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pushpitkc
How many integers less than 200 will have only 3 factors?

A. 2
B. 4
C. 6
D. 9
E. 12

Self-made

Numbers with 3 factors are squares of prime numbers. So, those squares are:

4, 9, 25, 49, 121, 169

So, there are six numbers less than 200 with only 3 factors.

Answer: C
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