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Question

Find the prime factorization of number 3584.

Answer

The prime factorization of 3584 is:

$$ 3584 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot7 $$

Which is the same as :

$$ 3584 = 2^{9}\cdot7 $$

Explanation

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

3584 can be written as 2 × 1792.
  • 3584
    • 2
    • 1792
1792 can be written as 2 × 896.
  • 3584
    • 2
    • 1792
      • 896
      • 2
896 can be written as 2 × 448.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
      • 2
448 can be written as 2 × 224.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
          • 2
      • 2
224 can be written as 2 × 112.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
            • 2
            • 112
          • 2
      • 2
112 can be written as 2 × 56.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
            • 2
            • 112
              • 56
              • 2
          • 2
      • 2
56 can be written as 2 × 28.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
            • 2
            • 112
              • 56
                • 2
                • 28
              • 2
          • 2
      • 2
28 can be written as 2 × 14.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
            • 2
            • 112
              • 56
                • 2
                • 28
                  • 14
                  • 2
              • 2
          • 2
      • 2
14 can be written as 2 × 7.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
            • 2
            • 112
              • 56
                • 2
                • 28
                  • 14
                    • 2
                    • 7
                  • 2
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 3584.
  • 3584
    • 2
    • 1792
      • 896
        • 2
        • 448
          • 224
            • 2
            • 112
              • 56
                • 2
                • 28
                  • 14
                    • 2
                    • 7
                  • 2
              • 2
          • 2
      • 2
This page was created using
Prime factorization calculator