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Question

Find the prime factorization of number 8000.

Answer

The prime factorization of 8000 is:

$$ 8000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 8000 = 2^{6}\cdot5^{3} $$

Explanation

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

8000 can be written as 10 × 800.
  • 8000
    • 10
    • 800
10 can be written as 2 × 5.
  • 8000
    • 10
      • 5
      • 2
    • 800
800 can be written as 10 × 80.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
      • 80
10 can be written as 2 × 5.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
        • 5
        • 2
      • 80
80 can be written as 10 × 8.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
        • 5
        • 2
      • 80
        • 10
        • 8
10 can be written as 2 × 5.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
        • 5
        • 2
      • 80
        • 10
          • 5
          • 2
        • 8
8 can be written as 2 × 4.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
        • 5
        • 2
      • 80
        • 10
          • 5
          • 2
        • 8
          • 2
          • 4
4 can be written as 2 × 2.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
        • 5
        • 2
      • 80
        • 10
          • 5
          • 2
        • 8
          • 2
          • 4
            • 2
            • 2
The end nodes are the prime factors of the number 8000.
  • 8000
    • 10
      • 5
      • 2
    • 800
      • 10
        • 5
        • 2
      • 80
        • 10
          • 5
          • 2
        • 8
          • 2
          • 4
            • 2
            • 2
This page was created using
Prime factorization calculator