The factors of 430 are listed after the puzzle.

What interesting fact could I say about the number 430? I did a little research.

Biblewheel.com quotes a verse from Galations 3:17 in the Bible: “And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was **four hundred and thirty **years after, cannot disannul, that it should make the promise of none effect.” Biblewheel states that 430 means the law, just as 666 means the beast.

Stetson.edu/numbers says that 430 “is the number of necklaces possible with 6 beads, each being one of 4 colors.” If I understood what that means in English, I’m sure I could construct it mathematically. I know it can’t mean 6 Choose 4. If you understand what it means, please comment.

Print the puzzles or type the factors on this excel file:10 Factors 2015-03-16

- 430 is a composite number.
- Prime factorization: 430 = 2 x 5 x 43
- 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 430 has exactly 8 factors.
- Factors of 430: 1, 2, 5, 10, 43, 86, 215, 430
- Factor pairs: 430 = 1 x 430, 2 x 215, 5 x 86, or 10 x 43
- 430 has no square factors that allow its square root to be simplified. √430 ≈ 20.7364

Comments on:"430 and Level 4" (4)mathtuition88said:Thanks for sharing the bible quote!

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ivasallaysaid:You’re welcome! I’m sure there are many more interesting numbers in the Bible, too.

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Steve Morrissaid:I’m struggling with that necklace thing. My first thought was 4^6 which is 4096. Then I thought, if each bead has to be a different colour to the adjacent bead, the number is 4*3^5, which is 972. You could halve that, on the grounds that half of the possible necklaces are the same but turned around, but that still gives you 486 possible necklaces.

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ivasallaysaid:If it just involved multiplication or powers, the formula would have to simplify to 2 x 5 x 43. http://en.wikipedia.org/wiki/Necklace_(combinatorics) seems to be about this topic, but I don’t understand it yet.

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