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Question

Find the prime factorization of number 3200.

Answer

The prime factorization of 3200 is:

$$ 3200 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5 $$

Which is the same as :

$$ 3200 = 2^{7}\cdot5^{2} $$

Explanation

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

3200 can be written as 10 × 320.
  • 3200
    • 10
    • 320
10 can be written as 2 × 5.
  • 3200
    • 10
      • 5
      • 2
    • 320
320 can be written as 10 × 32.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
      • 32
10 can be written as 2 × 5.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
        • 5
        • 2
      • 32
32 can be written as 2 × 16.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
        • 5
        • 2
      • 32
        • 2
        • 16
16 can be written as 2 × 8.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
        • 5
        • 2
      • 32
        • 2
        • 16
          • 8
          • 2
8 can be written as 2 × 4.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
        • 5
        • 2
      • 32
        • 2
        • 16
          • 8
            • 2
            • 4
          • 2
4 can be written as 2 × 2.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
        • 5
        • 2
      • 32
        • 2
        • 16
          • 8
            • 2
            • 4
              • 2
              • 2
          • 2
The end nodes are the prime factors of the number 3200.
  • 3200
    • 10
      • 5
      • 2
    • 320
      • 10
        • 5
        • 2
      • 32
        • 2
        • 16
          • 8
            • 2
            • 4
              • 2
              • 2
          • 2
This page was created using
Prime factorization calculator