A Multiplication Based Logic Puzzle

873 and Level 5

8 + 7 + 3 = 18; 1 + 8 = 9, so 873 can be evenly divided by 9.

27² + 12² = 873 so 873 is the hypotenuse of a Pythagorean triple:

  • 585-648-873 which is 9 times (65-72-97), and can be calculated from 27² – 12², 2(27)(12), 27² + 12²

Stetson.edu reminds us that 1! + 2! + 3! + 4! + 5! + 6! = 873.

Print the puzzles or type the solution on this excel file: 12 factors 864-874

  • 873 is a composite number.
  • Prime factorization: 873 = 3 × 3 × 97, which can be written 873 = 3² × 97
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 873 has exactly 6 factors.
  • Factors of 873: 1, 3, 9, 97, 291, 873
  • Factor pairs: 873 = 1 × 873, 3 × 291, or 9 × 97
  • Taking the factor pair with the largest square number factor, we get √873 = (√9)(√97) = 3√97 ≈ 29.546573

 

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Comments on: "873 and Level 5" (2)

  1. 27^2 x 12^2 is particularly appealing to me. It’s strange how different numbers feel different. I really like the factorial fact 1! + 2! + 3! + 4! + 5! + 6! …and 3√97 has a certain appeal too. 873. Yes, I like it.

    Liked by 1 person

  2. I love the way you love numbers!

    Like

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