A Multiplication Based Logic Puzzle

351 is the 26th triangular number. The only triangular numbers that are NOT composite numbers are 1 and 3. All other triangular numbers are composite numbers because they can be written as the product of two consecutive numbers divided by 2. For example, 351 can be written like this:

  • 1 + 2 + 3 + . . . + 24 + 25 + 26 = (26 x 27)/2 = 351

Also, 351 is divisible by 3 because 1, 3, 5 are three consecutive odd numbers. Since 3 is the middle number in that list, 351 is also divisible by 9. Scroll down past the puzzle to see the rest of 351’s factors.

351 Puzzle

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

  • 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 Factors

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