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Find the prime factorization of number 3840.

Answer

The prime factorization of 3840 is:

$$ 3840 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5 $$

Which is the same as :

$$ 3840 = 2^{8}\cdot3\cdot5 $$

Explanation

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

3840 can be written as 10 × 384.
  • 3840
    • 10
    • 384
10 can be written as 2 × 5.
  • 3840
    • 10
      • 5
      • 2
    • 384
384 can be written as 2 × 192.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
192 can be written as 2 × 96.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
        • 2
96 can be written as 2 × 48.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
          • 2
          • 48
        • 2
48 can be written as 2 × 24.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
          • 2
          • 48
            • 24
            • 2
        • 2
24 can be written as 2 × 12.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
          • 2
          • 48
            • 24
              • 2
              • 12
            • 2
        • 2
12 can be written as 2 × 6.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
          • 2
          • 48
            • 24
              • 2
              • 12
                • 6
                • 2
            • 2
        • 2
6 can be written as 2 × 3.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
          • 2
          • 48
            • 24
              • 2
              • 12
                • 6
                  • 2
                  • 3
                • 2
            • 2
        • 2
The end nodes are the prime factors of the number 3840.
  • 3840
    • 10
      • 5
      • 2
    • 384
      • 2
      • 192
        • 96
          • 2
          • 48
            • 24
              • 2
              • 12
                • 6
                  • 2
                  • 3
                • 2
            • 2
        • 2
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