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Question

Find the prime factorization of number 2160.

Answer

The prime factorization of 2160 is:

$$ 2160 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot5 $$

Which is the same as :

$$ 2160 = 2^{4}\cdot3^{3}\cdot5 $$

Explanation

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

2160 can be written as 10 × 216.
  • 2160
    • 10
    • 216
10 can be written as 2 × 5.
  • 2160
    • 10
      • 5
      • 2
    • 216
216 can be written as 2 × 108.
  • 2160
    • 10
      • 5
      • 2
    • 216
      • 2
      • 108
108 can be written as 2 × 54.
  • 2160
    • 10
      • 5
      • 2
    • 216
      • 2
      • 108
        • 54
        • 2
54 can be written as 2 × 27.
  • 2160
    • 10
      • 5
      • 2
    • 216
      • 2
      • 108
        • 54
          • 2
          • 27
        • 2
27 can be written as 3 × 9.
  • 2160
    • 10
      • 5
      • 2
    • 216
      • 2
      • 108
        • 54
          • 2
          • 27
            • 9
            • 3
        • 2
9 can be written as 3 × 3.
  • 2160
    • 10
      • 5
      • 2
    • 216
      • 2
      • 108
        • 54
          • 2
          • 27
            • 9
              • 3
              • 3
            • 3
        • 2
The end nodes are the prime factors of the number 2160.
  • 2160
    • 10
      • 5
      • 2
    • 216
      • 2
      • 108
        • 54
          • 2
          • 27
            • 9
              • 3
              • 3
            • 3
        • 2
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Prime factorization calculator