A Multiplication Based Logic Puzzle

678 and Level 5

678 is made from 3 consecutive numbers so it is divisible by 3. The middle number of those 3 consecutive numbers is not divisible by 3, so 678 is NOT divisible by 9.

678 is the hypotenuse of  Pythagorean triple 90-672-678. What is the greatest common factor of those 3 numbers?

678 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-11-09

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  • 678 is a composite number.
  • Prime factorization: 678 = 2 x 3 x 113
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 678 has exactly 8 factors.
  • Factors of 678: 1, 2, 3, 6, 113, 226, 339, 678
  • Factor pairs: 678 = 1 x 678, 2 x 339, 3 x 226, or 6 x 113
  • 678 has no square factors that allow its square root to be simplified. √678 ≈ 26.038433.

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678 Logic

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