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Find the prime factorization of number 256.

Answer

The prime factorization of 256 is:

$$ 256 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2 $$

Which is the same as :

$$ 256 = 2^{8} $$

Explanation

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

256 can be written as 2 × 128.
  • 256
    • 2
    • 128
128 can be written as 2 × 64.
  • 256
    • 2
    • 128
      • 64
      • 2
64 can be written as 2 × 32.
  • 256
    • 2
    • 128
      • 64
        • 2
        • 32
      • 2
32 can be written as 2 × 16.
  • 256
    • 2
    • 128
      • 64
        • 2
        • 32
          • 16
          • 2
      • 2
16 can be written as 2 × 8.
  • 256
    • 2
    • 128
      • 64
        • 2
        • 32
          • 16
            • 2
            • 8
          • 2
      • 2
8 can be written as 2 × 4.
  • 256
    • 2
    • 128
      • 64
        • 2
        • 32
          • 16
            • 2
            • 8
              • 4
              • 2
          • 2
      • 2
4 can be written as 2 × 2.
  • 256
    • 2
    • 128
      • 64
        • 2
        • 32
          • 16
            • 2
            • 8
              • 4
                • 2
                • 2
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 256.
  • 256
    • 2
    • 128
      • 64
        • 2
        • 32
          • 16
            • 2
            • 8
              • 4
                • 2
                • 2
              • 2
          • 2
      • 2
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