A Multiplication Based Logic Puzzle

570 and Level 6

570 is the hypotenuse of Pythagorean triple 342-456-570. What 3 digit number is the greatest common factor of those three numbers?

570 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-07-27

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  • 570 is a composite number.
  • Prime factorization: 570 = 2 x 3 x 5 x 19
  • The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 x 2 = 16. Therefore 570 has exactly 16 factors.
  • Factors of 570: 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
  • Factor pairs: 570 = 1 x 570, 2 x 285, 3 x 190, 5 x 114, 6 x 95, 10 x 57, 15 x 38, or 19 x 30
  • 570 has no square factors that allow its square root to be simplified. √570 ≈ 23.87467

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570 Logic

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