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

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stonecold
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If a positive integer n has 211 factors,then how many prime factors [#permalink] New post   08 Dec 2016, 02:39
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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
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stonecold
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Re: If a positive integer n has 211 factors,then how many prime factors [#permalink] 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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chetan2u
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Re: If a positive integer n has 211 factors,then how many prime factors [#permalink] 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] New post   14 Aug 2019, 18:49
chetan2u wrote:
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




Hi Chetan,

Can this be done with 6k+1?

So I did it like this, 211 is 6(35)+ 1.

As 1 is the only prime factor in the factor, so n has 1 prime factor...

Am I correct here?

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vitalik222
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Re: If a positive integer n has 211 factors,then how many prime factors [#permalink] New post   11 Apr 2022, 13:49
stonecold wrote:
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.


Could you help me please understand why we here not count number "1" as a second prime factor of the n?

I can't understand it...
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Re: If a positive integer n has 211 factors,then how many prime factors [#permalink] New post   14 Nov 2023, 14:33
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Re: If a positive integer n has 211 factors,then how many prime factors [#permalink]
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