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Question

Find the prime factorization of number 15984.

Answer

The prime factorization of 15984 is:

$$ 15984 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot37 $$

Which is the same as :

$$ 15984 = 2^{4}\cdot3^{3}\cdot37 $$

Explanation

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

15984 can be written as 2 × 7992.
  • 15984
    • 2
    • 7992
7992 can be written as 2 × 3996.
  • 15984
    • 2
    • 7992
      • 3996
      • 2
3996 can be written as 2 × 1998.
  • 15984
    • 2
    • 7992
      • 3996
        • 2
        • 1998
      • 2
1998 can be written as 2 × 999.
  • 15984
    • 2
    • 7992
      • 3996
        • 2
        • 1998
          • 999
          • 2
      • 2
999 can be written as 3 × 333.
  • 15984
    • 2
    • 7992
      • 3996
        • 2
        • 1998
          • 999
            • 3
            • 333
          • 2
      • 2
333 can be written as 3 × 111.
  • 15984
    • 2
    • 7992
      • 3996
        • 2
        • 1998
          • 999
            • 3
            • 333
              • 111
              • 3
          • 2
      • 2
111 can be written as 3 × 37.
  • 15984
    • 2
    • 7992
      • 3996
        • 2
        • 1998
          • 999
            • 3
            • 333
              • 111
                • 3
                • 37
              • 3
          • 2
      • 2
The end nodes are the prime factors of the number 15984.
  • 15984
    • 2
    • 7992
      • 3996
        • 2
        • 1998
          • 999
            • 3
            • 333
              • 111
                • 3
                • 37
              • 3
          • 2
      • 2
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