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Which of the following is the greatest common divisor of (n + 5) and (
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03 Jul 2023, 01:33
03 Jul 2023, 01:33
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Question Stats:
81% (00:39) correct
18% (00:52) wrong based on 11 sessions
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Which of the following is the greatest common divisor of \((n + 5)\) and \((n + 5)^2\), where n is a prime number?
A. 1
B. 5
C. n
D. (n + 5)
E. \((n + 5)^2\)
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
A. 1
B. 5
C. n
D. (n + 5)
E. \((n + 5)^2\)
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
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Re: Which of the following is the greatest common divisor of (n + 5) and (
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04 Jul 2023, 10:10
04 Jul 2023, 10:10
1
Expert Reply
Let's consider the expression (n+5) and (n+5)^2.
If n is a prime number, then (n+5) and (n+5)^2 will have a common factor of (n+5). In other words, (n+5) is a factor of (n+5)^2.
To find the greatest common divisor (GCD) of (n+5) and (n+5)^2, we need to determine if there are any additional factors beyond (n+5) that are common to both expressions.
Since n is a prime number, it means that there are no factors common to n and (n+5) other than 1 and (n+5) itself. Therefore, the GCD of (n+5) and (n+5)^2 is (n+5).
In conclusion, the greatest common divisor of (n+5) and (n+5)^2, where n is a prime number, is (n+5).
Answer: D
If n is a prime number, then (n+5) and (n+5)^2 will have a common factor of (n+5). In other words, (n+5) is a factor of (n+5)^2.
To find the greatest common divisor (GCD) of (n+5) and (n+5)^2, we need to determine if there are any additional factors beyond (n+5) that are common to both expressions.
Since n is a prime number, it means that there are no factors common to n and (n+5) other than 1 and (n+5) itself. Therefore, the GCD of (n+5) and (n+5)^2 is (n+5).
In conclusion, the greatest common divisor of (n+5) and (n+5)^2, where n is a prime number, is (n+5).
Answer: D
Re: Which of the following is the greatest common divisor of (n + 5) and (
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04 Jul 2023, 12:30
04 Jul 2023, 12:30
GeminiHeat wrote:
Since n is a prime number, it means that there are no factors common to n and (n+5) other than 1 and (n+5) itself.
I don't understand this portion of your explanation. Could you please tell me how did you get this?
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