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If a positive integer n has 211 factors,then how many prime factors

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If a positive integer n has 211 factors,then how many prime factors  [#permalink]

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New post 08 Dec 2016, 02:39
1
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A
B
C
D
E

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  65% (hard)

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Re: If a positive integer n has 211 factors,then how many prime factors  [#permalink]

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New post 08 Dec 2016, 05:16
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stonecold wrote:
If a positive integer n has 211 factors,then how many prime factors does n have?

A)one
B)two
C)three
D)Four
E)cannot be determined


Let the factor be a^x*b^y.....
So (x+1)(y+1).....=211..
Now 211 is a prime number...
So only one variable x or y is 210 and the others are 0..
(210+1)(0+1)...
So the number becomes a^210..
Thus only ONE prime factor is there..

A
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Re: If a positive integer n has 211 factors,then how many prime factors  [#permalink]

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New post 15 Jan 2017, 10:03
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Notice here that 211 is a prime number as it is not divisile by any prime factor less than or equal to the square root of 211.
Therefore the number n can only be of the form => Prime^210
Hence it will always have one prime factor.

If the number of factors of any integer is a prime number => The integer will always have a single prime factor.
Hence A.

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Re: If a positive integer n has 211 factors,then how many prime factors  [#permalink]

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New post 01 Sep 2018, 12:02
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Re: If a positive integer n has 211 factors,then how many prime factors   [#permalink] 01 Sep 2018, 12:02
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