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
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
答案是D，跪求好心人解释....
-- by 会员 camelo777 (2011/6/17 5:58:01)
k= 3^n * 7^m
(n+1)(m+1)=6
n=2, m=1 or m=2, n=1
1) n=2, then you can get k 2) m=/=2, then you can still get the value of k, which is the same as the one you get from 1)
唉，不要有这种负面的心理暗示，我21号二战，从几天前开始就不断进行正面的心理暗示，一战时就因为太紧张崩溃掉... 给你粘过来一个 Use the rule: For a given number all the combinations of its prime factors are factors of that number. K has 6 factors: 1, 3, 7, _, _, k (4 factors are known) 7x3 is also a factor by the above rule. so the factors are : 1, 3, 7, 21, _, k
Statement 1 3^2 is factor, so the last unknown factor is 9. so the factors are : 1, 3, 7, 21, 9, k There are two 3s and one 7 as prime factors: so the number is 3x3x7 = 63 SUFFICIENT
Statement 2 7^2 is NOT a factor of k. (so only one 7 as a primefactor). The missing factor will have to formed with other primefactor : so 3x3 is last missing factor. There are two 3 and one 7 as prime factors: so the number is 3x3x7 = 63 SUFFICIENT
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发表于 2011-6-17 05:58:01
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