1984 AMC 12 第 3 题

Question

令

n

为大于

1

、没有小于

10

的素因数的最小合数。则

Let

n

be the smallest nonprime integer greater than

1

with no prime factor less than

10.

Then

100\lt n\le110

110\lt n\le120

120\lt n\le130

130\lt n\le140

140\lt n\le150

允许的最小素因数为

11

The smallest permitted prime factor is

11

要得到最小合数，使用两个最小的允许素因数

To make the smallest composite, use the two smallest permitted prime factors

n

的每个素因数都至少为

11

。满足这一性质的最小合数是

11\cdot11=121

，它位于

120\lt n\le130

内。

所以正确答案是 C。

Every prime factor of

n

is at least

11.

The smallest composite with that property is

11\cdot11=121,

which lies in

120\lt n\le130.

Therefore, the correct answer is C.

其他年份的第 3 题