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Question

Find the prime factorization of number 20736.

Answer

The prime factorization of 20736 is:

$$ 20736 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3 $$

Which is the same as :

$$ 20736 = 2^{8}\cdot3^{4} $$

Explanation

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

20736 can be written as 2 × 10368.
  • 20736
    • 2
    • 10368
10368 can be written as 2 × 5184.
  • 20736
    • 2
    • 10368
      • 5184
      • 2
5184 can be written as 2 × 2592.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
      • 2
2592 can be written as 2 × 1296.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
          • 2
      • 2
1296 can be written as 2 × 648.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
          • 2
      • 2
648 can be written as 2 × 324.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
              • 2
          • 2
      • 2
324 can be written as 2 × 162.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
                • 2
                • 162
              • 2
          • 2
      • 2
162 can be written as 2 × 81.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
                • 2
                • 162
                  • 81
                  • 2
              • 2
          • 2
      • 2
81 can be written as 3 × 27.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
                • 2
                • 162
                  • 81
                    • 3
                    • 27
                  • 2
              • 2
          • 2
      • 2
27 can be written as 3 × 9.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
                • 2
                • 162
                  • 81
                    • 3
                    • 27
                      • 9
                      • 3
                  • 2
              • 2
          • 2
      • 2
9 can be written as 3 × 3.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
                • 2
                • 162
                  • 81
                    • 3
                    • 27
                      • 9
                        • 3
                        • 3
                      • 3
                  • 2
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 20736.
  • 20736
    • 2
    • 10368
      • 5184
        • 2
        • 2592
          • 1296
            • 2
            • 648
              • 324
                • 2
                • 162
                  • 81
                    • 3
                    • 27
                      • 9
                        • 3
                        • 3
                      • 3
                  • 2
              • 2
          • 2
      • 2
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Prime factorization calculator