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Question

Find the prime factorization of number 2592000.

Answer

The prime factorization of 2592000 is:

$$ 2592000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 2592000 = 2^{8}\cdot3^{4}\cdot5^{3} $$

Explanation

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

2592000 can be written as 10 × 259200.
  • 2592000
    • 10
    • 259200
10 can be written as 2 × 5.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
259200 can be written as 10 × 25920.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
      • 25920
10 can be written as 2 × 5.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
25920 can be written as 10 × 2592.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
        • 2592
10 can be written as 2 × 5.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
2592 can be written as 2 × 1296.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
1296 can be written as 2 × 648.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
            • 2
648 can be written as 2 × 324.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
            • 2
324 can be written as 2 × 162.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
                • 162
                • 2
            • 2
162 can be written as 2 × 81.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
                • 162
                  • 2
                  • 81
                • 2
            • 2
81 can be written as 3 × 27.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
                • 162
                  • 2
                  • 81
                    • 27
                    • 3
                • 2
            • 2
27 can be written as 3 × 9.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
                • 162
                  • 2
                  • 81
                    • 27
                      • 3
                      • 9
                    • 3
                • 2
            • 2
9 can be written as 3 × 3.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
                • 162
                  • 2
                  • 81
                    • 27
                      • 3
                      • 9
                        • 3
                        • 3
                    • 3
                • 2
            • 2
The end nodes are the prime factors of the number 2592000.
  • 2592000
    • 10
      • 5
      • 2
    • 259200
      • 10
        • 5
        • 2
      • 25920
        • 10
          • 5
          • 2
        • 2592
          • 2
          • 1296
            • 648
              • 2
              • 324
                • 162
                  • 2
                  • 81
                    • 27
                      • 3
                      • 9
                        • 3
                        • 3
                    • 3
                • 2
            • 2
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