numbers having 4 distinct prime factors

Question

What are the numbers that have at least four distinct prime factors up to $500$?

The first number is $210$ and the four factors are($2,3,5,7$) next number is $330 \ (2,3,5,11)$. what are the next numbers up to $500$?

Answer 1

In a problem like this, it's really just a matter of searching by hand until you find all combinations. One can limit the search by for instance checking things like

• What's the largest prime possible?
• Must $2$ be included?

and just go from there. Try to be as systematic as you can (going in ascending order might not be the best idea), and remember that $2\cdot 2\cdot 3\cdot 5\cdot 7 = 420$ is also valid. Good luck.