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Question

Find the prime factorization of number 1296.

Answer

The prime factorization of 1296 is:

$$ 1296 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3 $$

Which is the same as :

$$ 1296 = 2^{4}\cdot3^{4} $$

Explanation

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

1296 can be written as 2 × 648.
  • 1296
    • 2
    • 648
648 can be written as 2 × 324.
  • 1296
    • 2
    • 648
      • 324
      • 2
324 can be written as 2 × 162.
  • 1296
    • 2
    • 648
      • 324
        • 2
        • 162
      • 2
162 can be written as 2 × 81.
  • 1296
    • 2
    • 648
      • 324
        • 2
        • 162
          • 81
          • 2
      • 2
81 can be written as 3 × 27.
  • 1296
    • 2
    • 648
      • 324
        • 2
        • 162
          • 81
            • 3
            • 27
          • 2
      • 2
27 can be written as 3 × 9.
  • 1296
    • 2
    • 648
      • 324
        • 2
        • 162
          • 81
            • 3
            • 27
              • 9
              • 3
          • 2
      • 2
9 can be written as 3 × 3.
  • 1296
    • 2
    • 648
      • 324
        • 2
        • 162
          • 81
            • 3
            • 27
              • 9
                • 3
                • 3
              • 3
          • 2
      • 2
The end nodes are the prime factors of the number 1296.
  • 1296
    • 2
    • 648
      • 324
        • 2
        • 162
          • 81
            • 3
            • 27
              • 9
                • 3
                • 3
              • 3
          • 2
      • 2
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Prime factorization calculator