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Question

Find the prime factorization of number 46656.

Answer

The prime factorization of 46656 is:

$$ 46656 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3 $$

Which is the same as :

$$ 46656 = 2^{6}\cdot3^{6} $$

Explanation

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

46656 can be written as 2 × 23328.
  • 46656
    • 2
    • 23328
23328 can be written as 2 × 11664.
  • 46656
    • 2
    • 23328
      • 11664
      • 2
11664 can be written as 2 × 5832.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
      • 2
5832 can be written as 2 × 2916.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
          • 2
      • 2
2916 can be written as 2 × 1458.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
          • 2
      • 2
1458 can be written as 2 × 729.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
              • 2
          • 2
      • 2
729 can be written as 3 × 243.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
                • 3
                • 243
              • 2
          • 2
      • 2
243 can be written as 3 × 81.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
                • 3
                • 243
                  • 81
                  • 3
              • 2
          • 2
      • 2
81 can be written as 3 × 27.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
                • 3
                • 243
                  • 81
                    • 3
                    • 27
                  • 3
              • 2
          • 2
      • 2
27 can be written as 3 × 9.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
                • 3
                • 243
                  • 81
                    • 3
                    • 27
                      • 9
                      • 3
                  • 3
              • 2
          • 2
      • 2
9 can be written as 3 × 3.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
                • 3
                • 243
                  • 81
                    • 3
                    • 27
                      • 9
                        • 3
                        • 3
                      • 3
                  • 3
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 46656.
  • 46656
    • 2
    • 23328
      • 11664
        • 2
        • 5832
          • 2916
            • 2
            • 1458
              • 729
                • 3
                • 243
                  • 81
                    • 3
                    • 27
                      • 9
                        • 3
                        • 3
                      • 3
                  • 3
              • 2
          • 2
      • 2
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Prime factorization calculator