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Question

Find the prime factorization of number 96256.

Answer

The prime factorization of 96256 is:

$$ 96256 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot47 $$

Which is the same as :

$$ 96256 = 2^{11}\cdot47 $$

Explanation

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

96256 can be written as 2 × 48128.
  • 96256
    • 2
    • 48128
48128 can be written as 2 × 24064.
  • 96256
    • 2
    • 48128
      • 24064
      • 2
24064 can be written as 2 × 12032.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
      • 2
12032 can be written as 2 × 6016.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
          • 2
      • 2
6016 can be written as 2 × 3008.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
          • 2
      • 2
3008 can be written as 2 × 1504.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
              • 2
          • 2
      • 2
1504 can be written as 2 × 752.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
                • 2
                • 752
              • 2
          • 2
      • 2
752 can be written as 2 × 376.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
                • 2
                • 752
                  • 376
                  • 2
              • 2
          • 2
      • 2
376 can be written as 2 × 188.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
                • 2
                • 752
                  • 376
                    • 2
                    • 188
                  • 2
              • 2
          • 2
      • 2
188 can be written as 2 × 94.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
                • 2
                • 752
                  • 376
                    • 2
                    • 188
                      • 94
                      • 2
                  • 2
              • 2
          • 2
      • 2
94 can be written as 2 × 47.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
                • 2
                • 752
                  • 376
                    • 2
                    • 188
                      • 94
                        • 2
                        • 47
                      • 2
                  • 2
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 96256.
  • 96256
    • 2
    • 48128
      • 24064
        • 2
        • 12032
          • 6016
            • 2
            • 3008
              • 1504
                • 2
                • 752
                  • 376
                    • 2
                    • 188
                      • 94
                        • 2
                        • 47
                      • 2
                  • 2
              • 2
          • 2
      • 2
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