Some interesting factoring problems
I just discovered the website nonemptyset.com, which runs a free monthly math contest for middle schoolers. It’s not as professional as something like Mathcounts, but it looks like at worst it might be a nice source of interesting problems. They have a few “lessons” available, and I enjoyed the factoring problems from Lesson I: Primes, Factorization, and Prime Factorization. If you are doing work on prime factorizations with your students, you might enjoy using some of those. You’d want to have first taught them how to find the number of factors any given number has, from its prime factorization.
Sadly, I do not “win at life” (as they said I would if I could find the smallest number with exactly 12 factors) since I only came up with the second-smallest such number on my first try. 😉