1323 Christmas Tree

 

If you start at the top of this Christmas tree puzzle and work your way down, you can find all the factors that make this puzzle work like a multiplication table.

Print the puzzles or type the solution in this excel file:10-factors-1321-1332

Here are some facts about the number 1323:

  • 1323 is a composite number.
  • Prime factorization: 1323 = 3 × 3 × 3 × 7 × 7, which can be written 1323 = 3³ × 7²
  • The exponents in the prime factorization are 3 and 2. Adding one to each and multiplying we get (3 + 1)(2 + 1) = 4 × 3 = 12. Therefore 1323 has exactly 12 factors.
  • Factors of 1323: 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323
  • Factor pairs: 1323 = 1 × 1323, 3 × 441, 7 × 189, 9 × 147, 21 × 63, or 27 × 49
  • Taking the factor pair with the largest square number factor, we get √1323 = (√441)(√3) = 21√3 ≈ 36.37307

 

Here is my favorite of the many possible factor trees for 1323:

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