A Multiplication Based Logic Puzzle

835 and Level 1

835 is the hypotenuse of a Pythagorean triple, 501-668-835, which is 167 times (3-4-5).

835 can be written as the difference of two squares two different ways:

  • 418² – 417² = 835
  • 86² – 81² = 835

835 can be written as the sum of consecutive numbers three different ways.

  • 417 + 418 = 835; that’s two consecutive numbers.
  • 165 + 166 + 167 + 168 + 169 = 835; that’s five consecutive numbers.
  • 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 = 835; that’s ten consecutive numbers.

Print the puzzles or type the solution on this excel file: 10-factors-835-842

  • 835 is a composite number.
  • Prime factorization: 835 = 5 × 167
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 835 has exactly 4 factors.
  • Factors of 835: 1, 5, 167, 835
  • Factor pairs: 835 = 1 × 835 or 5 × 167
  • 835 has no square factors that allow its square root to be simplified. √835 ≈ 28.89636655

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