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16 Sep 2014, 01:07
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If \(x\) is a prime number, what is the greatest factor of \(x^2\)?
(1) \(x^2\) is an odd number
(2) The greatest common factor of \(x\) and 6 is 3
(1) \(x^2\) is an odd number
(2) The greatest common factor of \(x\) and 6 is 3
16 Sep 2014, 01:07
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Official Solution:
If \(x\) is a prime number, what is the greatest factor of \(x^2\)?
Remember, the greatest factor of any positive integer is the integer itself. For instance, the greatest factor of 10 is 10. So, the greatest factor of \(x^2\) will be \(x^2\) itself, which means we need to determine the value of \(x\) to answer the question.
(1) \(x^2\) is an odd number.
This statement just tells us that \(x\) could be any prime except 2. This, however, is insufficient to establish a specific numerical value for \(x\).
(2) The greatest common factor of \(x\) and 6 is 3.
Given that \(x\) is a prime number, this implies \(x=3\) (as no other prime number can have 3 as a factor). Therefore, the greatest factor of \(x^2=9\) is 9. Sufficient.
Answer: B
If \(x\) is a prime number, what is the greatest factor of \(x^2\)?
Remember, the greatest factor of any positive integer is the integer itself. For instance, the greatest factor of 10 is 10. So, the greatest factor of \(x^2\) will be \(x^2\) itself, which means we need to determine the value of \(x\) to answer the question.
(1) \(x^2\) is an odd number.
This statement just tells us that \(x\) could be any prime except 2. This, however, is insufficient to establish a specific numerical value for \(x\).
(2) The greatest common factor of \(x\) and 6 is 3.
Given that \(x\) is a prime number, this implies \(x=3\) (as no other prime number can have 3 as a factor). Therefore, the greatest factor of \(x^2=9\) is 9. Sufficient.
Answer: B
25 Jul 2023, 07:35
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
