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08 Dec 2016, 02:39
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
53% (01:38) correct
47%
(01:23)
wrong
based on 344
sessions
History
Date
Time
Result
Not Attempted Yet
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
A)one
B)two
C)three
D)Four
E)cannot be determined
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.
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.
General Discussion
08 Dec 2016, 05:16
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stonecold
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
