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Question

Find the prime factorization of number 17640.

Answer

The prime factorization of 17640 is:

$$ 17640 = 2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot7\cdot7 $$

Which is the same as :

$$ 17640 = 2^{3}\cdot3^{2}\cdot5\cdot7^{2} $$

Explanation

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

17640 can be written as 10 × 1764.
  • 17640
    • 10
    • 1764
10 can be written as 2 × 5.
  • 17640
    • 10
      • 5
      • 2
    • 1764
1764 can be written as 2 × 882.
  • 17640
    • 10
      • 5
      • 2
    • 1764
      • 2
      • 882
882 can be written as 2 × 441.
  • 17640
    • 10
      • 5
      • 2
    • 1764
      • 2
      • 882
        • 441
        • 2
441 can be written as 3 × 147.
  • 17640
    • 10
      • 5
      • 2
    • 1764
      • 2
      • 882
        • 441
          • 3
          • 147
        • 2
147 can be written as 3 × 49.
  • 17640
    • 10
      • 5
      • 2
    • 1764
      • 2
      • 882
        • 441
          • 3
          • 147
            • 49
            • 3
        • 2
49 can be written as 7 × 7.
  • 17640
    • 10
      • 5
      • 2
    • 1764
      • 2
      • 882
        • 441
          • 3
          • 147
            • 49
              • 7
              • 7
            • 3
        • 2
The end nodes are the prime factors of the number 17640.
  • 17640
    • 10
      • 5
      • 2
    • 1764
      • 2
      • 882
        • 441
          • 3
          • 147
            • 49
              • 7
              • 7
            • 3
        • 2
This page was created using
Prime factorization calculator