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Question

Find the prime factorization of number 320000.

Answer

The prime factorization of 320000 is:

$$ 320000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 320000 = 2^{9}\cdot5^{4} $$

Explanation

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

320000 can be written as 10 × 32000.
  • 320000
    • 10
    • 32000
10 can be written as 2 × 5.
  • 320000
    • 10
      • 5
      • 2
    • 32000
32000 can be written as 10 × 3200.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
      • 3200
10 can be written as 2 × 5.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
3200 can be written as 10 × 320.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
        • 320
10 can be written as 2 × 5.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
320 can be written as 10 × 32.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
          • 32
10 can be written as 2 × 5.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
            • 5
            • 2
          • 32
32 can be written as 2 × 16.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
            • 5
            • 2
          • 32
            • 2
            • 16
16 can be written as 2 × 8.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
            • 5
            • 2
          • 32
            • 2
            • 16
              • 8
              • 2
8 can be written as 2 × 4.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
            • 5
            • 2
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
              • 2
4 can be written as 2 × 2.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
            • 5
            • 2
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
                  • 2
                  • 2
              • 2
The end nodes are the prime factors of the number 320000.
  • 320000
    • 10
      • 5
      • 2
    • 32000
      • 10
        • 5
        • 2
      • 3200
        • 10
          • 5
          • 2
        • 320
          • 10
            • 5
            • 2
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
                  • 2
                  • 2
              • 2
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Prime factorization calculator