A Multiplication Based Logic Puzzle

3 + 5 + 1 = 9, a number divisible by both 3 and 9, so 351 is divisible by both 3 and 9 and is a composite number. Scroll down past the puzzle to see 351’s factors.

351 Puzzle

  • 351 is a composite number.
  • Prime factorization: 351 = 3 x 3 x 3 x 13, which can be written (3^3) x 13
  • The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 351 has exactly 8 factors.
  • Factors of 351: 1, 3, 9, 13, 27, 39, 117, 351
  • Factor pairs: 351 = 1 x 351, 3 x 117, 9 x 39, or 13 x 27
  • Taking the factor pair with the largest square number factor, we get √351 = (√9)(√39) = 3√39 ≈ 18.735
  • 351 is a triangular number. 1 + 2 + 3 + . . . + 24 + 25 + 26 = (26 x 27)/2 = 351

Print the puzzles or type the factors on this excel file: 12 Factors 2015-01-12

351 Factors

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