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Question

Find the prime factorization of number 729.

Answer

The prime factorization of 729 is:

$$ 729 = 3\cdot3\cdot3\cdot3\cdot3\cdot3 $$

Which is the same as :

$$ 729 = 3^{6} $$

Explanation

Prime factorization can be nicely visualized by creating a factorization tree.

729 can be written as 3 × 243.
  • 729
    • 3
    • 243
243 can be written as 3 × 81.
  • 729
    • 3
    • 243
      • 81
      • 3
81 can be written as 3 × 27.
  • 729
    • 3
    • 243
      • 81
        • 3
        • 27
      • 3
27 can be written as 3 × 9.
  • 729
    • 3
    • 243
      • 81
        • 3
        • 27
          • 9
          • 3
      • 3
9 can be written as 3 × 3.
  • 729
    • 3
    • 243
      • 81
        • 3
        • 27
          • 9
            • 3
            • 3
          • 3
      • 3
The end nodes are the prime factors of the number 729.
  • 729
    • 3
    • 243
      • 81
        • 3
        • 27
          • 9
            • 3
            • 3
          • 3
      • 3
This page was created using
Prime factorization calculator