- 219 is a composite number.
- Prime factorization: 219 = 3 x 73
- The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1) x (1 + 1) = 2 x 2 = 4. Therefore 219 has 4 factors.
- Factors of 219: 1, 3, 73, 219
- Factor pairs: 219 = 1 x 219 or 3 x 73
- 219 has no square factors so its square root cannot be simplified. √219 ≈ 14.799

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-09-01

Your fourth bullet point, about the exponents, is completely new to me. I don’t really get it yet, but I’m working on it!

I guess I’ll have to write a better explanation soon.