A Multiplication Based Logic Puzzle

Since this site is called Find the Factors and each post is numbered, I factor those numbers and write some interesting facts about them.

For example, this is my 698th post, so I’ll give its factoring information here:

  • 698 is a composite number.
  • Prime factorization: 698 = 2 x 349
  • 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 698 has exactly 4 factors.
  • Factors of 698: 1, 2, 349, 698
  • Factor pairs: 698 = 1 x 698 or 2 x 349
  • 698 has no square factors that allow its square root to be simplified. √698 ≈ 26.4196896. (Close to the beginning of the square root we see 698 backwards as well as the magic number 689.)

Now I’ll share some other interesting information about the number 698:

698 is the hypotenuse of Pythagorean triple 360-598-698.

Stetson.edu informs us that 3^2 + 4^3 + 5^4 = 698.

173 + 174 + 175 + 176 = 698 so it is the sum of four consecutive numbers.

698 is a palindrome in two different bases:

  • 22322 BASE 4; note 2(256) + 2(64) + 3(16) + 2(4) + 2(1) = 698
  • 585 BASE 11; note 5(121) + 8(11) + 5(1) = 698

And 698 is a permutation of 689, the number of my most viewed post of all time. I wrote that post a week ago on Tuesday, and all it contained was some interesting information about the number 689. There was nothing earth shattering in it.

However, Wednesday evening, Denise Gaskins shared that 689th post on her facebook page, Let’s Play Math. (She has so many good things on her facebook page.)

689 Let's Play Math

The 17 shares you see on this facebook post is NOT the whole picture; it is only the beginning.

Other than my homepage/archives, my most viewed post has now become “What Makes 689 Amazing” It has also been shared on facebook over 2000 times!

Top Posts all time

Here is the breakdown of the number of views it received each day:

Number of Views Per Day

Usually most of my views come from the United States and the United Kingdom, but there was a definite although temporary shift last week. Here are the four top counties viewing this blog from last Thursday to Sunday:

Blog Views

I was quite puzzled by why this blog post went viral in Hong Kong and Taiwan. Perhaps Alan Parr’s (wbhs1962) comment about a funny experience with the number 689 broke the ice. Eventually a few readers from Hong Kong and Taiwan enlightened me about the viral interest in this particular number. Those comments were all quite fascinating and an educational experience for me. I invite you to read them as well.


Comments on: "698 The week a single post went viral in two countries" (4)

  1. You just never know what will be popular! Hooray for magic numbers!

    Liked by 1 person

  2. Neat adventure. Congratulations on having it. I hope the return to normal isn’t too hard … I’m recovering from my own very brief discovery. I think I’m all right (sniff).

    Liked by 1 person

    • Thank you. Returning to normal has been fine. I’m used to it. If going viral had lasted for a few months and then went back to normal that probably would be much more difficult.

      Liked by 1 person

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