4 + 1 + 7 = 12, a multiple of three, so 417 can be evenly divided by three. Its other factors are listed below the puzzle.

The colors for today’s puzzle use the same key that puzzle 414 used and 422 will use, even though none of the squares here are blue. If I had colored the actual number 417, it would be blue. Also if I colored the number 414 it would have been green.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-03-02

- 417 is a composite number.
- Prime factorization: 417 = 3 x 139
- The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 417 has exactly 4 factors.
- Factors of 417: 1, 3, 139, 417
- Factor pairs: 417 = 1 x 417 or 3 x 139
- 417 has no square factors that allow its square root to be simplified. √417 ≈ 20.4206

it’s intriguing indeed to read the abstract within the dearth of the subject knowledge i own … coaxing me through another land unseen .. so not familiar — like being in a dream of numbered skies or squared sighs … what i don’t know i fill in spaces with whatever i please … a montage of meaning … i see more … in my view … than those who know who see .,.. your work is not beyond understanding for those of us who do not know your language … it’s not just yours or yours or yours …. … it’s all mine sublime and personal …. and i thoroughly enjoy the freedom to see through my own spectacles the poetry you give .. thanks for reading my numbers too … ks …

I especially like the line “like being in a dream of numbered skies or squared sighs.”

Thank you for opening my eyes to the poetry of numbers.

Well the yellow numbers are all even, and so are the greens. The blues are odd, which means that they are the product of two odd numbers. Hmm, but the yellows are sometimes the product of an odd and even number and sometimes of two even numbers. Bah.

You’re on the right track, although I wasn’t exactly thinking even or odd for any of the numbers. Perhaps I should also say that 145 and many other numbers would not have any color at all.