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Question

Find the prime factorization of number 512.

Answer

The prime factorization of 512 is:

$$ 512 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2 $$

Which is the same as :

$$ 512 = 2^{9} $$

Explanation

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

512 can be written as 2 × 256.
  • 512
    • 2
    • 256
256 can be written as 2 × 128.
  • 512
    • 2
    • 256
      • 128
      • 2
128 can be written as 2 × 64.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
      • 2
64 can be written as 2 × 32.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
          • 32
          • 2
      • 2
32 can be written as 2 × 16.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
          • 2
      • 2
16 can be written as 2 × 8.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
              • 2
          • 2
      • 2
8 can be written as 2 × 4.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
              • 2
          • 2
      • 2
4 can be written as 2 × 2.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
                  • 2
                  • 2
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 512.
  • 512
    • 2
    • 256
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
                  • 2
                  • 2
              • 2
          • 2
      • 2
This page was created using
Prime factorization calculator