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Question

Find the prime factorization of number 540.

Answer

The prime factorization of 540 is:

$$ 540 = 2\cdot2\cdot3\cdot3\cdot3\cdot5 $$

Which is the same as :

$$ 540 = 2^{2}\cdot3^{3}\cdot5 $$

Explanation

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

540 can be written as 10 × 54.
  • 540
    • 10
    • 54
10 can be written as 2 × 5.
  • 540
    • 10
      • 5
      • 2
    • 54
54 can be written as 2 × 27.
  • 540
    • 10
      • 5
      • 2
    • 54
      • 2
      • 27
27 can be written as 3 × 9.
  • 540
    • 10
      • 5
      • 2
    • 54
      • 2
      • 27
        • 9
        • 3
9 can be written as 3 × 3.
  • 540
    • 10
      • 5
      • 2
    • 54
      • 2
      • 27
        • 9
          • 3
          • 3
        • 3
The end nodes are the prime factors of the number 540.
  • 540
    • 10
      • 5
      • 2
    • 54
      • 2
      • 27
        • 9
          • 3
          • 3
        • 3
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Prime factorization calculator