1287 Mystery Level

I’ve put twenty clues in this mystery level puzzle. Some of the factors will be easy to find, but some of them won’t be quite as easy. Use logic the entire time, and you will be able to solve it!

Print the puzzles or type the solution in this excel file: 10-factors-1281-1288

Now I’ll share some facts about the number 1287:

  • 1287 is a composite number.
  • Prime factorization: 1287 = 3 × 3 × 11 × 13, which can be written 1287 = 3² × 11 × 13
  • 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 1287 has exactly 12 factors.
  • Factors of 1287: 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287
  • Factor pairs: 1287 = 1 × 1287, 3 × 429, 9 × 143, 11 × 117, 13 × 99, or 33 × 39
  • Taking the factor pair with the largest square number factor, we get √1287 = (√9)(√143) = 3√143 ≈ 35.87478

1287 is the hypotenuse of a Pythagorean triple:
495-1188-1287 which is (5-12-13) times 99

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