A Multiplication Based Logic Puzzle

614 and Level 6

I learned from Stetson.edu that 614 is the smallest integer that can be expressed as the sum of 3 squares 9 different ways. I decided to see if I could find those 9 ways. Here they are:

614 is the sum of 3 squares 9 different ways

614 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-09-07

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  • 614 is a composite number.
  • Prime factorization: 614 = 2 x 307
  • 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 614 has exactly 4 factors.
  • Factors of 614: 1, 2, 307, 614
  • Factor pairs: 614 = 1 x 614 or 2 x 307
  • 614 has no square factors that allow its square root to be simplified. √614 ≈ 24.77902

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614 Logic

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Comments on: "614 and Level 6" (1)

  1. […] 614 can also be expressed as the sum of 3 squares 9 different ways, but one of those ways is 17² + 17² + 6² = 614, and that duplicates one of the square numbers. […]

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