A Multiplication Based Logic Puzzle

469 and Level 4

469 is the short leg in the Pythagorean triple 469-1608-1675. What is the greatest common factor of those three numbers? Hint: Don’t let the larger numbers scare you; the greatest common factor is a factor of 469, the smallest of those three numbers, and its factors are listed below the puzzle.

469 Puzzle

Print the puzzles or type the solution on this excel file:  12 Factors 2015-04-20


  • 469 is a composite number.
  • Prime factorization: 469 = 7 x 67
  • 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 469 has exactly 4 factors.
  • Factors of 469: 1, 7, 67, 469
  • Factor pairs: 469 = 1 x 469 or 7 x 67
  • 469 has no square factors that allow its square root to be simplified. √469 ≈ 21.6564


469 Logic


Comments on: "469 and Level 4" (4)

  1. Yes I was scared until I read your hint.
    You made this one quite easy..
    Is it unusual for Pythagorean triplets to a have common factor?

    Liked by 1 person

    • ivasallay said:

      That’s a very good question!
      If the Pythagorean triple is primitive, the greatest common factor will be 1.
      However, if it is not a primitive, the three numbers will always have a greatest common factor that is greater than 1.

      I think I’ll write a post or two about this topic. Thanks!

      Liked by 1 person

      • So it’s all or nothing!?!
        I look forward to your post about this. I’m especially curious about the lingo: is there an opposite word for the primitive in terms of Pythagorean triplets? I’ll wait for your post to find out. thank you.

        Liked by 1 person

        • ivasallay said:

          As far as I can tell, the opposite of primitive is simply non-primitive.
          Thank you for your curiosity!


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