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For how many positive integer values of x is an integer?
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12 Aug 2018, 15:23
12 Aug 2018, 15:23
1
Expert Reply
00:00
Question Stats:
87% (00:34) correct
12% (00:33) wrong based on 54 sessions
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Re: For how many positive integer values of x is an integer?
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15 Aug 2018, 05:06
15 Aug 2018, 05:06
Expert Reply
Explanation
If x is a positive integer such that \(\frac{65}{x}\) is also an integer, then x must be a factor of 65. The factors of 65 are 1, 5, 13, and 65. Thus, there are four positive integer values of x such that \(\frac{65}{x}\) is an integer.
If x is a positive integer such that \(\frac{65}{x}\) is also an integer, then x must be a factor of 65. The factors of 65 are 1, 5, 13, and 65. Thus, there are four positive integer values of x such that \(\frac{65}{x}\) is an integer.
Re: For how many positive integer values of x is an integer?
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20 Feb 2023, 19:08
20 Feb 2023, 19:08
1
(1) Prime factor 65: 5^1 * 13^ 1
(2) Take the exponents and add +1 to each prime number: (1+1)*(1+1)
(3) (2)(2) = 4
(2) Take the exponents and add +1 to each prime number: (1+1)*(1+1)
(3) (2)(2) = 4
