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Question

Find the prime factorization of number 2073600.

Answer

The prime factorization of 2073600 is:

$$ 2073600 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5 $$

Which is the same as :

$$ 2073600 = 2^{10}\cdot3^{4}\cdot5^{2} $$

Explanation

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

2073600 can be written as 10 × 207360.
  • 2073600
    • 10
    • 207360
10 can be written as 2 × 5.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
207360 can be written as 10 × 20736.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
      • 20736
10 can be written as 2 × 5.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
20736 can be written as 2 × 10368.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
10368 can be written as 2 × 5184.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
          • 2
5184 can be written as 2 × 2592.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
            • 2
            • 2592
          • 2
2592 can be written as 2 × 1296.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
            • 2
            • 2592
              • 1296
              • 2
          • 2
1296 can be written as 2 × 648.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
            • 2
            • 2592
              • 1296
                • 2
                • 648
              • 2
          • 2
648 can be written as 2 × 324.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
            • 2
            • 2592
              • 1296
                • 2
                • 648
                  • 324
                  • 2
              • 2
          • 2
324 can be written as 2 × 162.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
            • 2
            • 2592
              • 1296
                • 2
                • 648
                  • 324
                    • 2
                    • 162
                  • 2
              • 2
          • 2
162 can be written as 2 × 81.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 20736
        • 2
        • 10368
          • 5184
            • 2
            • 2592
              • 1296
                • 2
                • 648
                  • 324
                    • 2
                    • 162
                      • 81
                      • 2
                  • 2
              • 2
          • 2
81 can be written as 3 × 27.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 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.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 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.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 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 2073600.
  • 2073600
    • 10
      • 5
      • 2
    • 207360
      • 10
        • 5
        • 2
      • 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