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Which of the following is divisible by an odd number of diff

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Which of the following is divisible by an odd number of diff [#permalink] New post   21 May 2019, 11:39
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Which of the following is divisible by an odd number of different positive integers?

Indicate all possible numbers.

A. 9

B. 17

C. 24

D. 36

E. 42
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A,D
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Re: Which of the following is divisible by an odd number of diff [#permalink] New post   26 May 2019, 07:52
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Which of the following is divisible by an odd number of different positive integers?

Indicate all possible numbers.

Only perfect squares have an odd number of factors, since factors are inherently paired and only a perfect square includes a factor paired with itself to create a redundant factor pair.

Only 9 and 36 are perfect squares available in the choices. Select Choices A and D.
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Re: Which of the following is divisible by an odd number of diff [#permalink] New post   07 Jun 2019, 22:43
the question confused me !
So, basically , it asks that what number ( as in the options) has odd number of positive factors, right?
Now, it is really easy as has been explained above. Thanks for the explanation
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Re: Which of the following is divisible by an odd number of diff [#permalink] New post   08 Jun 2019, 07:40
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jelal123 wrote:
the question confused me !
So, basically , it asks that what number ( as in the options) has odd number of positive factors, right?
Now, it is really easy as has been explained above. Thanks for the explanation

I'm glad you found the explanation helpful!
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Re: Which of the following is divisible by an odd number of diff [#permalink] New post   25 Sep 2024, 15:52
jelal123 wrote:
the question confused me !
So, basically , it asks that what number ( as in the options) has odd number of positive factors, right?
Now, it is really easy as has been explained above. Thanks for the explanation



Still Bit COnfused..?? Can You Please Explain..?
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Re: Which of the following is divisible by an odd number of diff [#permalink] New post   26 Sep 2024, 02:38
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The right answer(s) for this question must have an odd number of factors in order to be divisible by an odd number of different positive integers. First, eliminate any prime numbers since they are divisible only by themselves and 1. (B) 17 is a prime number. Now check the remaining choices. The factors of 9 are 1, 3, and 9, so (A) is a correct choice. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 for a total of 8, so eliminate (C). The distinct factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36 for a total of 9, so (D) is a correct choice. Finally, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Since there are 8 factors, (E) is incorrect. The correct choices are (A) and (D).
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Re: Which of the following is divisible by an odd number of diff [#permalink]
26 Sep 2024, 02:38
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