A Multiplication Based Logic Puzzle

860 and Level 6

Print the puzzles or type the solution on this excel file: 10-factors-853-863

860 is the hypotenuse of a Pythagorean triple: 516-688-860, which is (3-4-5) times 172.

860 can be written as the sum of four consecutive prime numbers: 199 + 211 + 223 + 227 = 860

  • 860 is a composite number.
  • Prime factorization: 860 = 2 × 2 × 5 × 43, which can be written 860 = 2² × 5 × 43
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 860 has exactly 12 factors.
  • Factors of 860: 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860
  • Factor pairs: 860 = 1 × 860, 2 × 430, 4 × 215, 5 × 172, 10 × 86, or 20 × 43,
  • Taking the factor pair with the largest square number factor, we get √860 = (√4)(√215) = 2√215 ≈ 29.3257566

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