343 and a Few Changes

Starting today, I’ve made a few small changes to the way my posts will look. If you can spot what the changes are, let me know if you have an opinion about them.

Quick Prime or Composite Number Test: If you divide 2^343 by 343, the remainder is 324, not 2, so 343 is NOT a prime number and is a composite number. (Use the mod function on the computer’s calculator to find the remainder.) Scroll down to see 343’s factors.

343 Puzzle

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-05

  • 343 is a composite number.
  • Prime factorization: 343 = 7 x 7 x 7, which can be written 343 = 7³
  • The exponent in the prime factorization is 3. Adding one, we get (3 + 1) = 4. Therefore 343 has exactly 4 factors.
  • Factors of 343: 1, 7, 49, 343
  • Factor pairs: 343 = 1 x 343 or 7 x 49
  • Taking the factor pair with the largest square number factor, we get √343 = (√7)(√49) = 7√7 ≈ 18.520
  • 343 is a perfect cube.

OEIS.org tells us that (3+4)³ = 343, so 343 is a Friedman number, a number that can be expressed using only its own digits and (), +, -, ×, and ÷.

343 Factors

6 thoughts on “343 and a Few Changes

  1. Hmmm, you’ve brought the puzzle up higher in your post and I think your side bar has changed, too, Seems to me the comments sections is higher up, which is nice as it gives a splash of color to the opening look of your post.

    • I guess I’ve given the impression that I did so much more than I really did. Sorry about that. I did make the first change you mentioned, but not the other two.

    • Thank you for your feedback. This was one of the changes that I thought might not make everyone happy. In the past my goal was to hide the answers for a week, but sometimes it was more like 3 weeks. I made this particular change to be more consistent, but because you said something about it, I will hide the answer for one day. I can still be consistent doing that.

      • Don’t make a change just because of me! Ask around first. Maybe you could include a link like “click here to see the solution” rather than display it on the same page? If people see it, it is hard not to look.

        • I think giving the solution the next day will work fine, (and it doesn’t involve anything I don’t know how to do.) Newspapers publish all kinds of puzzles. Some puzzles give the answer the same day, and some give the answer the next day.

          People will still have to scroll down to see the solution.

          For levels 4, 5, & 6, I plan on only giving a table showing a logical way to arrive at the correct answer.

          If the device you use has a spreadsheet program such as excel, you can access the puzzles at the beginning of the week and work on them without the solution being available for several days, too.

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