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Question

Find the prime factorization of number 448.

Answer

The prime factorization of 448 is:

$$ 448 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot7 $$

Which is the same as :

$$ 448 = 2^{6}\cdot7 $$

Explanation

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

448 can be written as 2 × 224.
  • 448
    • 2
    • 224
224 can be written as 2 × 112.
  • 448
    • 2
    • 224
      • 112
      • 2
112 can be written as 2 × 56.
  • 448
    • 2
    • 224
      • 112
        • 2
        • 56
      • 2
56 can be written as 2 × 28.
  • 448
    • 2
    • 224
      • 112
        • 2
        • 56
          • 28
          • 2
      • 2
28 can be written as 2 × 14.
  • 448
    • 2
    • 224
      • 112
        • 2
        • 56
          • 28
            • 2
            • 14
          • 2
      • 2
14 can be written as 2 × 7.
  • 448
    • 2
    • 224
      • 112
        • 2
        • 56
          • 28
            • 2
            • 14
              • 7
              • 2
          • 2
      • 2
The end nodes are the prime factors of the number 448.
  • 448
    • 2
    • 224
      • 112
        • 2
        • 56
          • 28
            • 2
            • 14
              • 7
              • 2
          • 2
      • 2
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Prime factorization calculator