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M20-02. If x is a prime number, what is the greatest factor

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Math Expert
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M20-02. If x is a prime number, what is the greatest factor [#permalink]  23 May 2014, 08:51
Expert's post
m20 q02

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
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Math Expert
Joined: 02 Sep 2009
Posts: 29856
Followers: 4925

Kudos [?]: 53970 [0], given: 8260

Re: M20-02. If x is a prime number, what is the greatest factor [#permalink]  23 May 2014, 08:57
Expert's post
Official Solution:

If $$x$$ is a prime number, what is the greatest factor of $$x^2$$?

Note that the greatest factor of a positive integer is that positive integer itself. For example the greatest factor of 10 is 10 itself. So, basically we should find 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 but 2, so it's clearly insufficient to determine the single numerical value of $$x$$.

(2) The greatest common factor of $$x$$ and 6 is 3. Since $$x$$ is a prime number then $$x=3$$ (no other prime can have 3 as a factor), so the greatest factor of $$x^2=9$$ is 9. Sufficient,

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Re: M20-02. If x is a prime number, what is the greatest factor   [#permalink] 23 May 2014, 08:57
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M20-02. If x is a prime number, what is the greatest factor

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