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Question

Find the prime factorization of number 144000.

Answer

The prime factorization of 144000 is:

$$ 144000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 144000 = 2^{7}\cdot3^{2}\cdot5^{3} $$

Explanation

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

144000 can be written as 10 × 14400.
  • 144000
    • 10
    • 14400
10 can be written as 2 × 5.
  • 144000
    • 10
      • 5
      • 2
    • 14400
14400 can be written as 10 × 1440.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
      • 1440
10 can be written as 2 × 5.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
1440 can be written as 10 × 144.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
        • 144
10 can be written as 2 × 5.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
144 can be written as 2 × 72.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
          • 2
          • 72
72 can be written as 2 × 36.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
          • 2
          • 72
            • 36
            • 2
36 can be written as 2 × 18.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
          • 2
          • 72
            • 36
              • 2
              • 18
            • 2
18 can be written as 2 × 9.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
          • 2
          • 72
            • 36
              • 2
              • 18
                • 9
                • 2
            • 2
9 can be written as 3 × 3.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
          • 2
          • 72
            • 36
              • 2
              • 18
                • 9
                  • 3
                  • 3
                • 2
            • 2
The end nodes are the prime factors of the number 144000.
  • 144000
    • 10
      • 5
      • 2
    • 14400
      • 10
        • 5
        • 2
      • 1440
        • 10
          • 5
          • 2
        • 144
          • 2
          • 72
            • 36
              • 2
              • 18
                • 9
                  • 3
                  • 3
                • 2
            • 2
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Prime factorization calculator