Question

What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?

$3127$

$3133$

$3137$

$3139$

$3149$

Video solution:

Click to load, then click again to play

Written solution:

The number is composite, not prime, and has no prime factor below $50$ . The smallest possible prime factors are therefore $53$ , $59$ , $61$ , and so on.

A square such as $53^2$ is not allowed, and $53^3$ is much larger than $53\cdot59$ . The smallest allowed nonsquare composite is $53\cdot59=3127$ .

Thus, the answer is A .

2012 AMC 8 Problem 18

Video solution:

Written solution:

Problem 18 in Other Years