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# How many of the integers from 1 to 16, inclusive, have 3

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How many of the integers from 1 to 16, inclusive, have 3 [#permalink]

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20 Sep 2008, 11:37
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How many of the integers from 1 to 16, inclusive, have 3 different factors?

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VP
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Re: PS [#permalink]

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20 Sep 2008, 12:53
vivektripathi wrote:
How many of the integers from 1 to 16, inclusive, have 3 different factors?

1 thru 16 inclusive are 16 numbers.

Any number that is prime will have that number and 1 as factors.

Numbers we need= 16 - (number of primes between 1 & 16)

primes between 1 & 16= 1,2,3,5,7,11,13 = 7

So numbers we need =9

All these numbers have at least 3 different factors. For example 8 has 1, 2, 4 & 8

9 has 1, 3 & 9

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Re: PS [#permalink]

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20 Sep 2008, 12:54
stallone wrote:
i think 3 , as 1 is also a factor

only squares of prime numbers have 3 factors..so based on that only 2 numbers from 1 to 16 have exactly 3 factors..4 and 9..

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VP
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Re: PS [#permalink]

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20 Sep 2008, 12:57
fresinha12 wrote:
stallone wrote:
i think 3 , as 1 is also a factor

only squares of prime numbers have 3 factors..so based on that only 2 numbers from 1 to 16 have exactly 3 factors..4 and 9..

Why are you looking for exactly 3?? The Q says 3 different factors ( 3 or more ) not exactly 3 different factors.

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VP
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Re: PS [#permalink]

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20 Sep 2008, 23:55
icandy wrote:
fresinha12 wrote:
stallone wrote:
i think 3 , as 1 is also a factor

only squares of prime numbers have 3 factors..so based on that only 2 numbers from 1 to 16 have exactly 3 factors..4 and 9..

Why are you looking for exactly 3?? The Q says 3 different factors ( 3 or more ) not exactly 3 different factors.

Eve i find difficulty in getting the Quant questions !!!meaning is vague!!!
How to prac on this !!!
_________________

cheers
Its Now Or Never

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Re: PS [#permalink]

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21 Sep 2008, 09:20
I took the question to mean 'have 3 different factors' as only 3... not more

Answer is 2 (9, 4)

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Re: PS   [#permalink] 21 Sep 2008, 09:20
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# How many of the integers from 1 to 16, inclusive, have 3

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