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标题: 一个数学题，哪位NN进来解释一下 [打印本页]

作者: ciscogeek 时间: 2008-2-18 22:23
标题: 一个数学题，哪位NN进来解释一下

How many numbers that are not divisible by 6 divide evenly into 264,600?

(A) 9
(B) 36
(C) 51
(D) 63
(E) 72

ok, long shot but here goes...

264600 = 2^3 * 5^2 * 3^3 * 7^2

The numbers that are not divisible by 6 should either not have a 3 or not
have a 2 in it as the product would yield a multiple of 6.

Combinations are 5^x*7^y*3^z and 5^x*7^y*2^z

Combinations for 5^2 * 7^2 * 3^3 = 3 * 3 * 4 = 36
(i.e. take 5^0, 5^1, 5^2 - 3 factors etc.)

Similarly, combinations for 5^2 * 7^2 * 2^3 = 3 * 3 * 4 = 36

Adding up, we get 72.

Out of this, we have to prune duplicates as 2^0 = 3^0 = 1. Total of
3*3 (possible powers of 5 * possible powers of 7) = 9

So, total = 72 - 9 = 63

作者: heslaw 时间: 2008-2-18 22:56

楼主的帖子里面的解释就很清楚啊

就是factorize 264600

然后在没有2x3的情况下找组合

最后减掉9是因为那9种情况下，我们会弄成0次方，从而造成重复，因为，任何数0次方都是1

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