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Question

Find the prime factorization of number 12800.

Answer

The prime factorization of 12800 is:

$$ 12800 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5 $$

Which is the same as :

$$ 12800 = 2^{9}\cdot5^{2} $$

Explanation

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

12800 can be written as 10 × 1280.
  • 12800
    • 10
    • 1280
10 can be written as 2 × 5.
  • 12800
    • 10
      • 5
      • 2
    • 1280
1280 can be written as 10 × 128.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
      • 128
10 can be written as 2 × 5.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
128 can be written as 2 × 64.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
64 can be written as 2 × 32.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
          • 32
          • 2
32 can be written as 2 × 16.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
          • 2
16 can be written as 2 × 8.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
              • 2
          • 2
8 can be written as 2 × 4.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
              • 2
          • 2
4 can be written as 2 × 2.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
                  • 2
                  • 2
              • 2
          • 2
The end nodes are the prime factors of the number 12800.
  • 12800
    • 10
      • 5
      • 2
    • 1280
      • 10
        • 5
        • 2
      • 128
        • 2
        • 64
          • 32
            • 2
            • 16
              • 8
                • 2
                • 4
                  • 2
                  • 2
              • 2
          • 2
This page was created using
Prime factorization calculator