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Question

Find the prime factorization of number 1872.

Answer

The prime factorization of 1872 is:

$$ 1872 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot13 $$

Which is the same as :

$$ 1872 = 2^{4}\cdot3^{2}\cdot13 $$

Explanation

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

1872 can be written as 2 × 936.
  • 1872
    • 2
    • 936
936 can be written as 2 × 468.
  • 1872
    • 2
    • 936
      • 468
      • 2
468 can be written as 2 × 234.
  • 1872
    • 2
    • 936
      • 468
        • 2
        • 234
      • 2
234 can be written as 2 × 117.
  • 1872
    • 2
    • 936
      • 468
        • 2
        • 234
          • 117
          • 2
      • 2
117 can be written as 3 × 39.
  • 1872
    • 2
    • 936
      • 468
        • 2
        • 234
          • 117
            • 3
            • 39
          • 2
      • 2
39 can be written as 3 × 13.
  • 1872
    • 2
    • 936
      • 468
        • 2
        • 234
          • 117
            • 3
            • 39
              • 13
              • 3
          • 2
      • 2
The end nodes are the prime factors of the number 1872.
  • 1872
    • 2
    • 936
      • 468
        • 2
        • 234
          • 117
            • 3
            • 39
              • 13
              • 3
          • 2
      • 2
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Prime factorization calculator