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Find the prime factorization of number 288.

Answer

The prime factorization of 288 is:

$$ 288 = 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3 $$

Which is the same as :

$$ 288 = 2^{5}\cdot3^{2} $$

Explanation

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

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