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Question

Find the prime factorization of number 1536.

Answer

The prime factorization of 1536 is:

$$ 1536 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3 $$

Which is the same as :

$$ 1536 = 2^{9}\cdot3 $$

Explanation

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

1536 can be written as 2 × 768.
  • 1536
    • 2
    • 768
768 can be written as 2 × 384.
  • 1536
    • 2
    • 768
      • 384
      • 2
384 can be written as 2 × 192.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
      • 2
192 can be written as 2 × 96.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
          • 2
      • 2
96 can be written as 2 × 48.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
            • 2
            • 48
          • 2
      • 2
48 can be written as 2 × 24.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
            • 2
            • 48
              • 24
              • 2
          • 2
      • 2
24 can be written as 2 × 12.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
            • 2
            • 48
              • 24
                • 2
                • 12
              • 2
          • 2
      • 2
12 can be written as 2 × 6.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
            • 2
            • 48
              • 24
                • 2
                • 12
                  • 6
                  • 2
              • 2
          • 2
      • 2
6 can be written as 2 × 3.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
            • 2
            • 48
              • 24
                • 2
                • 12
                  • 6
                    • 2
                    • 3
                  • 2
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 1536.
  • 1536
    • 2
    • 768
      • 384
        • 2
        • 192
          • 96
            • 2
            • 48
              • 24
                • 2
                • 12
                  • 6
                    • 2
                    • 3
                  • 2
              • 2
          • 2
      • 2
This page was created using
Prime factorization calculator