求助prep上一道关于factor的题目

fighting2012

The positive integer k has exactly two positive prime factors, 3 and 7.  If k has a total of 6 positive factors, including 1 and k, what is the value of k ?

(1) 3^2 is a factor of k.

(2) 7^2 is not a factor of k.

选D

各种不懂啊，球NN指导

sdcar2010

it's not 32, but 3^2
it's not 72, but 7^2.

MarsTOF

it's not 32, but 3^2
it's not 72, but 7^2.

-- by 会员 sdcar2010 (2011/6/24 21:37:40)

fighting2012

it's not 32, but 3^2
it's not 72, but 7^2.

-- by 会员 sdcar2010 (2011/6/24 21:37:40)

啊啊~是的。。。不好意思贴的时候忘记改了。。。

不过这样的题事后看着答案能套出来，可是考场上考到肯定就晕倒了。。

sdcar2010

Well, this question is rather simple.

We know that 1, 3, 7, and K are 4 out of 6 factors of K. So we are missing two more factors. Without even looking at the answers, you know that you only need one more prime factor, either 3 or 7 to complete the roster of 6 factors, since that extra prime factor itself and its product with the other prime factor will be the two missing factors!

So if the answer choice gives you the extra 3 or 7, it would be sufficient. Otherwise, insufficient.

fighting2012

Well, this question is rather simple.

We know that 1, 3, 7, and K are 4 out 6 factors of K. So we are missing two more factors. Without even looking at the answers, you know that you only need one more prime factor, either 3 or 7 to complete the roster of 6 factors, since that extra prime factor itself and its product with the other prime factor will be the two missing factors!

So if the answer choice gives you the extra 3 or 7, it would be sufficient. Otherwise, insufficient.

-- by 会员 sdcar2010 (2011/6/25 9:00:23)

谢谢NN指导！明白了，其实就是在考还需要几个prime factor才能得到6个factors
现在想想，当初我就是误以为需要两个extra prime factor才能构成 6个factors，所以选错了。。
多年不碰数学，这个factor什么的总是搞混。。。

不过那两个factor 应该是那个extra factor和3或者7的乘积吧~不是那个extra prime factor itself and its product with the other prime factor。因为3或者7已经给出了啊~

sdcar2010

You are right.