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How many numbers less than 200 will have only 3 factors?

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pushpitkc
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How many numbers less than 200 will have only 3 factors? [#permalink] New post   06 Jun 2018, 11:58
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How many integers less than 200 will have only 3 factors?

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

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C
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ishan92
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Re: How many numbers less than 200 will have only 3 factors? [#permalink] New post   06 Jun 2018, 13:11
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pushpitkc wrote:
How many integers less than 200 will have only 3 factors?

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

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All numbers of the form p^2, where p is a prime number will have 3 factors.
So the numbers are,
4=2^2
9=3^3
25=5^5
49=7^7
121=11^11
169=13^13

Total=6 (C)
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How many numbers less than 200 will have only 3 factors? [#permalink] New post   06 Jun 2018, 13:34
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The only integers that have 3 factors are squares of prime numbers:

4, 9, 25, 49, 121, 169

Answer (C)
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Re: How many numbers less than 200 will have only 3 factors? [#permalink] New post   06 Jun 2018, 16:34
pushpitkc wrote:
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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Re: How many numbers less than 200 will have only 3 factors? [#permalink] New post   16 Aug 2020, 03:29
pushpitkc wrote:
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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Re: How many numbers less than 200 will have only 3 factors? [#permalink] New post   27 Apr 2023, 17:50
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pushpitkc wrote:
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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gmatclubot
Re: How many numbers less than 200 will have only 3 factors? [#permalink]
27 Apr 2023, 17:50
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