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Question

Find the prime factorization of number 259200.

Answer

The prime factorization of 259200 is:

$$ 259200 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5 $$

Which is the same as :

$$ 259200 = 2^{7}\cdot3^{4}\cdot5^{2} $$

Explanation

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

259200 can be written as 10 × 25920.
  • 259200
    • 10
    • 25920
10 can be written as 2 × 5.
  • 259200
    • 10
      • 5
      • 2
    • 25920
25920 can be written as 10 × 2592.
  • 259200
    • 10
      • 5
      • 2
    • 25920
      • 10
      • 2592
10 can be written as 2 × 5.
  • 259200
    • 10
      • 5
      • 2
    • 25920
      • 10
        • 5
        • 2
      • 2592
2592 can be written as 2 × 1296.
  • 259200
    • 10
      • 5
      • 2
    • 25920
      • 10
        • 5
        • 2
      • 2592
        • 2
        • 1296
1296 can be written as 2 × 648.
  • 259200
    • 10
      • 5
      • 2
    • 25920
      • 10
        • 5
        • 2
      • 2592
        • 2
        • 1296
          • 648
          • 2
648 can be written as 2 × 324.
  • 259200
    • 10
      • 5
      • 2
    • 25920
      • 10
        • 5
        • 2
      • 2592
        • 2
        • 1296
          • 648
            • 2
            • 324
          • 2
324 can be written as 2 × 162.
  • 259200
    • 10
      • 5
      • 2
    • 25920
      • 10
        • 5
        • 2
      • 2592
        • 2
        • 1296
          • 648
            • 2
            • 324
              • 162
              • 2
          • 2
162 can be written as 2 × 81.
  • 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.
  • 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.
  • 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.
  • 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 259200.
  • 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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