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Question

Find the prime factorization of number 51200.

Answer

The prime factorization of 51200 is:

$$ 51200 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5 $$

Which is the same as :

$$ 51200 = 2^{11}\cdot5^{2} $$

Explanation

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

51200 can be written as 10 × 5120.
  • 51200
    • 10
    • 5120
10 can be written as 2 × 5.
  • 51200
    • 10
      • 5
      • 2
    • 5120
5120 can be written as 10 × 512.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
      • 512
10 can be written as 2 × 5.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
512 can be written as 2 × 256.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
256 can be written as 2 × 128.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
          • 128
          • 2
128 can be written as 2 × 64.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
          • 128
            • 2
            • 64
          • 2
64 can be written as 2 × 32.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
          • 128
            • 2
            • 64
              • 32
              • 2
          • 2
32 can be written as 2 × 16.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
          • 128
            • 2
            • 64
              • 32
                • 2
                • 16
              • 2
          • 2
16 can be written as 2 × 8.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
          • 128
            • 2
            • 64
              • 32
                • 2
                • 16
                  • 8
                  • 2
              • 2
          • 2
8 can be written as 2 × 4.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 512
        • 2
        • 256
          • 128
            • 2
            • 64
              • 32
                • 2
                • 16
                  • 8
                    • 2
                    • 4
                  • 2
              • 2
          • 2
4 can be written as 2 × 2.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 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 51200.
  • 51200
    • 10
      • 5
      • 2
    • 5120
      • 10
        • 5
        • 2
      • 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