A Multiplication Based Logic Puzzle

323 and Level 1

  • 323 is a composite number.
  • Prime factorization: 323 = 17 x 19
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 323 has exactly 4 factors.
  • Factors of 323: 1, 17, 19, 323
  • Factor pairs: 323 = 1 x 323 or 17 x 19
  • 323 has no square factors that allow its square root to be simplified. √323 ≈ 17.972

Since 17 × 19 = 323, we know that 323 + 1 = 324 = 18². That follows from the fact that (n – 1)(n + 1) = n² – 1 is ALWAYS true.

Because 17 is one of its factors, 323 is the hypotenuse of a Pythagorean triple:

  • 152-285-323 which is 19 times 8-15-17

Here’s 20 very easy clues to help you solve this puzzle:

2014-50 Level 1

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-15

2014-50 Level 1 Factors

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