A Multiplication Based Logic Puzzle

294 and Level 5

  • 294 is a composite number.
  • Prime factorization: 294 = 2 x 3 x 7 x 7, which can be written 294 = 2 x 3 x (7^2)
  • The exponents in the prime factorization are 1, 1 and 2. Adding one to each and multiplying we get (1 + 1)(1 + 1)(2 + 1) = 2 x 2 x 3 = 12. Therefore 294 has exactly 12 factors.
  • Factors of 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
  • Factor pairs: 294 = 1 x 294, 2 x 147, 3 x 98, 6 x 49, 7 x 42, or 14 x 21
  • Taking the factor pair with the largest square number factor, we get √294 = (√6)(√49) = 7√6 ≈ 17.146

Can you fill out this multiplication table that has only eleven clues?

2014-45 Level 5

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-10

2014-45 Level 5 Logic

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