AMC 8 2012 Problem 18
AMC8 2012 年第 18 题
整除与因数★★★☆☆
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
有一个正整数，既不是质数，也不是完全平方数，且没有小于 50 的质因数。那么符合要求的最小正整数是多少？
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正确答案 · Correct Answer
A
解析 · Solution
Solution 1
The problem states that the answer cannot be a perfect square or have prime factors less than 50. Therefore, the answer will be the product of at least two different primes greater than 50. The two smallest primes greater than 50 are 53 and 59. Multiplying these two primes, we obtain the number 3127, which is also the smallest number on the list of answer choices. So we are done, and the answer is 3127.
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