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Find the prime factorization of number 800.

Answer

The prime factorization of 800 is:

$$ 800 = 2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5 $$

Which is the same as :

$$ 800 = 2^{5}\cdot5^{2} $$

Explanation

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

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