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Find the prime factorization of number 576.

Answer

The prime factorization of 576 is:

$$ 576 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3 $$

Which is the same as :

$$ 576 = 2^{6}\cdot3^{2} $$

Explanation

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

576 can be written as 2 × 288.
  • 576
    • 2
    • 288
288 can be written as 2 × 144.
  • 576
    • 2
    • 288
      • 144
      • 2
144 can be written as 2 × 72.
  • 576
    • 2
    • 288
      • 144
        • 2
        • 72
      • 2
72 can be written as 2 × 36.
  • 576
    • 2
    • 288
      • 144
        • 2
        • 72
          • 36
          • 2
      • 2
36 can be written as 2 × 18.
  • 576
    • 2
    • 288
      • 144
        • 2
        • 72
          • 36
            • 2
            • 18
          • 2
      • 2
18 can be written as 2 × 9.
  • 576
    • 2
    • 288
      • 144
        • 2
        • 72
          • 36
            • 2
            • 18
              • 9
              • 2
          • 2
      • 2
9 can be written as 3 × 3.
  • 576
    • 2
    • 288
      • 144
        • 2
        • 72
          • 36
            • 2
            • 18
              • 9
                • 3
                • 3
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 576.
  • 576
    • 2
    • 288
      • 144
        • 2
        • 72
          • 36
            • 2
            • 18
              • 9
                • 3
                • 3
              • 2
          • 2
      • 2
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