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: