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Question

Find the prime factorization of number 11664.

Answer

The prime factorization of 11664 is:

$$ 11664 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3 $$

Which is the same as :

$$ 11664 = 2^{4}\cdot3^{6} $$

Explanation

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

11664 can be written as 2 × 5832.
  • 11664
    • 2
    • 5832
5832 can be written as 2 × 2916.
  • 11664
    • 2
    • 5832
      • 2916
      • 2
2916 can be written as 2 × 1458.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
      • 2
1458 can be written as 2 × 729.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
          • 2
      • 2
729 can be written as 3 × 243.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
            • 3
            • 243
          • 2
      • 2
243 can be written as 3 × 81.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
            • 3
            • 243
              • 81
              • 3
          • 2
      • 2
81 can be written as 3 × 27.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
            • 3
            • 243
              • 81
                • 3
                • 27
              • 3
          • 2
      • 2
27 can be written as 3 × 9.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
            • 3
            • 243
              • 81
                • 3
                • 27
                  • 9
                  • 3
              • 3
          • 2
      • 2
9 can be written as 3 × 3.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
            • 3
            • 243
              • 81
                • 3
                • 27
                  • 9
                    • 3
                    • 3
                  • 3
              • 3
          • 2
      • 2
The end nodes are the prime factors of the number 11664.
  • 11664
    • 2
    • 5832
      • 2916
        • 2
        • 1458
          • 729
            • 3
            • 243
              • 81
                • 3
                • 27
                  • 9
                    • 3
                    • 3
                  • 3
              • 3
          • 2
      • 2
This page was created using
Prime factorization calculator