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Question

Find the prime factorization of number 4200.

Answer

The prime factorization of 4200 is:

$$ 4200 = 2\cdot2\cdot2\cdot3\cdot5\cdot5\cdot7 $$

Which is the same as :

$$ 4200 = 2^{3}\cdot3\cdot5^{2}\cdot7 $$

Explanation

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

4200 can be written as 10 × 420.
  • 4200
    • 10
    • 420
10 can be written as 2 × 5.
  • 4200
    • 10
      • 5
      • 2
    • 420
420 can be written as 10 × 42.
  • 4200
    • 10
      • 5
      • 2
    • 420
      • 10
      • 42
10 can be written as 2 × 5.
  • 4200
    • 10
      • 5
      • 2
    • 420
      • 10
        • 5
        • 2
      • 42
42 can be written as 2 × 21.
  • 4200
    • 10
      • 5
      • 2
    • 420
      • 10
        • 5
        • 2
      • 42
        • 2
        • 21
21 can be written as 3 × 7.
  • 4200
    • 10
      • 5
      • 2
    • 420
      • 10
        • 5
        • 2
      • 42
        • 2
        • 21
          • 7
          • 3
The end nodes are the prime factors of the number 4200.
  • 4200
    • 10
      • 5
      • 2
    • 420
      • 10
        • 5
        • 2
      • 42
        • 2
        • 21
          • 7
          • 3
This page was created using
Prime factorization calculator