2012 AMC 8 Problems/Problem 18
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What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
Solution
The problem states that the answer cannot be a perfect square or have prime factors less than . Therefore, the answer will be the product of at least two different primes grater than
. The two smallest primes greater than
are
and
. Multiplying these two primes, we obtain the number
, which is also the smallest number on the list of answer choices. So we are done, and the answer is
.
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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All AJHSME/AMC 8 Problems and Solutions |