It’s easy to see that 663 is divisible by three.

That may not be very interesting at all, but…..

Because 13 and 17, 663’s other two prime factors, have a remainder of one when each is divided by four, 663 is the hypotenuse of FOUR Pythagorean triples. Can you find the greatest common factor of each triple?

- 420-513-663
- 63-660-663
- 255-612-663
- 312-585-663

—————————————————————————————————

Art is not one of my strongest skills, but here is my attempt to make a puzzle that looks like a peanut butter kiss, a traditional Halloween candy:

Color can be inviting, but it can also be distracting. Here is the same puzzle without the added color:

Print the puzzles or type the solution on this excel file: 10 Factors 2015-10-26

—————————————————————————————————

- 663 is a composite number.
- Prime factorization: 663 = 3 x 13 x 17
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 663 has exactly 8 factors.
- Factors of 663: 1, 3, 13, 17, 39, 51, 221, 663
- Factor pairs: 663 = 1 x 663, 3 x 221, 13 x 51, or 17 x 39
- 663 has no square factors that allow its square root to be simplified. √663 ≈ 25.748786.

—————————————————————————————————

Thank you for sharing the solution, Ricardo, and happy Halloween:

```
```@findthefactors done. Happy Halloween there. pic.twitter.com/v3n0tm6IgZ

— riccardo (@ricca9380) October 31, 2015

//platform.twitter.com/widgets.js