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For how many positive integers is the number of positive divisors

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For how many positive integers is the number of positive divisors  [#permalink]

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New post 23 Apr 2016, 07:11
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A
B
C
D
E

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  35% (medium)

Question Stats:

57% (00:39) correct 43% (00:30) wrong based on 76 sessions

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For how many positive integers is the number of positive divisors equal to the number itself ?
[A] none
[B] one
[C] two
[D] three
[E] cannot be determined

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Re: For how many positive integers is the number of positive divisors  [#permalink]

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New post 23 Apr 2016, 20:29
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1 and 2 are the only integers that have the number of positive factors equal to the number itself.

Answer: C
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For how many positive integers is the number of factors equal to the n  [#permalink]

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New post 20 Jul 2016, 09:50
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Re: For how many positive integers is the number of factors equal to the n  [#permalink]

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New post 20 Jul 2016, 10:05
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stonecold wrote:
For how many positive integers is the number of factors equal to the number itself?
A) one
B) two
C) three
D) four
E) cannot be determined


Start TESTING values.

The factors of 1: {1}. 1 factor. WORKS!
The factors of 2: {1,2}, 2 factors. WORKS!
The factors of 3: {1,3}, 2 factors. Doesn't work
The factors of 4: {1,2,4}, 3 factors. Doesn't work

As we can see, if an integer n has n factors, then the factors of n must be: {1, 2, 3,....., n)
So, we can quickly see that the only positive integers that meet this criterion are 1 and 2

Answer:
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Re: For how many positive integers is the number of positive divisors  [#permalink]

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New post 14 Aug 2017, 03:37
Clearly C
the 2 numbers are 1 and 2 with same number of positive divisors in number as the integer value itself..

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Re: For how many positive integers is the number of positive divisors &nbs [#permalink] 14 Aug 2017, 03:37
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