请教一道数学-因子数

sophia417 · 发表于 2009-2-19 22:25:00

How many different prime numbers are factors of the positive intergers?

i four different prime numbers are factors of 2n.

ii four different prime numbers are factors of n^2

选B。不是很明白题目。是说2n里面有4个不同的质数还是说2n是由4个不同质数组成的？

在者，应该怎么去考虑这道题目呢？

谢谢～^^

prayerv · 发表于 2010-11-19 10:44:16

。。。我顶一下刚好也想问这题来着。。

2不懂怎么分析

n^2的因子数不是三个吗？

prayerv · 发表于 2010-11-19 11:49:26

crystal9006 · 发表于 2010-11-19 11:51:32

因为（i）不能说明2是否是n的一个质因数所以可能是4个可能是5个

而（ii）中n^2的质因数个数和n 相同都是4个~~

sdcar2010 · 发表于 2010-11-19 12:04:31

It is better to read the question as the following:

How many different prime numbers are factors of the positive interger N?

i four different prime numbers are factors of 2N.

ii four different prime numbers are factors of N^2

(i) N could have 4 prime number factors if N is even; N could have 3 prime number factors if N is odd.
(ii) Since N^2 = N * N, N would have the same number of prime number factors as N^2. Hence, N has 4 different prime number factors.

prayerv · 发表于 2010-11-19 12:33:14

It is better to read the question as the following:

How many different prime numbers are factors of the positive interger N?

i four different prime numbers are factors of 2N.

ii four different prime numbers are factors of N^2

(i) N could have 4 prime number factors if N is even; N could have 3 prime number factors if N is odd.
(ii) Since N^2 = N * N, N would have the same number of prime number factors as N^2. Hence, N has 4 different prime number factors.

-- by 会员 sdcar2010 (2010/11/19 12:04:31)

谢谢就想知道N^2的prime factors数为什么是4？？？我痴呆了。。。。。。 - -

crystal9006 · 发表于 2010-11-19 17:30:47

n不一定是prime number~~

请教一道数学-因子数

请教一道数学-因子数

所属分类: GMAT考试

正在浏览此版块的会员 ()

浏览过的版块