A Multiplication Based Logic Puzzle

There is a lot of road construction near my house. I don’t know if it is related, but the outside cable that provides us internet connection died sometime on the morning of Sunday, 23 August 2015.

That broken cable line meant that we had no home phone service, no internet, no banking information, no twitter, no facebook = no looking at the latest pictures of my grandchildren, no reading Blogspot, no watching Netflix or Youtube, and no reading or writing on WordPress.

I don’t have a smart phone, but my husband uses the Wifi in our house for his. His smart phone wasn’t smart enough to switch to our phone’s data plan. Instead it relentlessly tried to connect to the Wifi every time either of us tried to use it.

My dead internet connection meant that if you were looking for information about the number 592 (and who isn’t), you had to wait a few days:

___________________________________

592 is a palindrome in three bases:

  • 727 BASE 9 because 7(81) + 2(9) + 7(1) = 592
  • 414 BASE 12 because 4(144) + 1(12) + 4(1) = 592
  • GG BASE 36 (G is 16 in base 10) because 16(36) + 16(1) = 592

592 is the hypotenuse of the Pythagorean triple 192-560-592. Which factor of 592 is the greatest common factor of those three numbers?

  • 592 is a composite number.
  • Prime factorization: 592 = 2 x 2 x 2 x 2 x 37, which can be written 592 = (2^4) x 37
  • The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 x 2 = 10. Therefore 592 has exactly 10 factors.
  • Factors of 592: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
  • Factor pairs: 592 = 1 x 592, 2 x 296, 4 x 148, 8 x 74, or 16 x 37
  • Taking the factor pair with the largest square number factor, we get √592 = (√16)(√37) = 4√37 ≈ 24.33105

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Comments on: "592 and The Broken Internet Connection" (4)

  1. Glad you’re back! What on earth did you do without access to any of life’s essentials? 🙂

    Liked by 1 person

    • Yeah, I know life wasn’t over because my internet was out. I still did all the things I usually do except look at other people’s posts.

      Like

  2. So glad you’re not dead! And that your internet is back! I bet those quiet days were sort of nice…as long as it was a temporary situation. 🙂

    Liked by 1 person

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