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Question

Find the prime factorization of number 7000.

Answer

The prime factorization of 7000 is:

$$ 7000 = 2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot7 $$

Which is the same as :

$$ 7000 = 2^{3}\cdot5^{3}\cdot7 $$

Explanation

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

7000 can be written as 10 × 700.
  • 7000
    • 10
    • 700
10 can be written as 2 × 5.
  • 7000
    • 10
      • 5
      • 2
    • 700
700 can be written as 10 × 70.
  • 7000
    • 10
      • 5
      • 2
    • 700
      • 10
      • 70
10 can be written as 2 × 5.
  • 7000
    • 10
      • 5
      • 2
    • 700
      • 10
        • 5
        • 2
      • 70
70 can be written as 10 × 7.
  • 7000
    • 10
      • 5
      • 2
    • 700
      • 10
        • 5
        • 2
      • 70
        • 10
        • 7
10 can be written as 2 × 5.
  • 7000
    • 10
      • 5
      • 2
    • 700
      • 10
        • 5
        • 2
      • 70
        • 10
          • 5
          • 2
        • 7
The end nodes are the prime factors of the number 7000.
  • 7000
    • 10
      • 5
      • 2
    • 700
      • 10
        • 5
        • 2
      • 70
        • 10
          • 5
          • 2
        • 7
This page was created using
Prime factorization calculator