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Question

Find the prime factorization of number 9990.

Answer

The prime factorization of 9990 is:

$$ 9990 = 2\cdot3\cdot3\cdot3\cdot5\cdot37 $$

Which is the same as :

$$ 9990 = 2\cdot3^{3}\cdot5\cdot37 $$

Explanation

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

9990 can be written as 10 × 999.
  • 9990
    • 10
    • 999
10 can be written as 2 × 5.
  • 9990
    • 10
      • 5
      • 2
    • 999
999 can be written as 3 × 333.
  • 9990
    • 10
      • 5
      • 2
    • 999
      • 3
      • 333
333 can be written as 3 × 111.
  • 9990
    • 10
      • 5
      • 2
    • 999
      • 3
      • 333
        • 111
        • 3
111 can be written as 3 × 37.
  • 9990
    • 10
      • 5
      • 2
    • 999
      • 3
      • 333
        • 111
          • 3
          • 37
        • 3
The end nodes are the prime factors of the number 9990.
  • 9990
    • 10
      • 5
      • 2
    • 999
      • 3
      • 333
        • 111
          • 3
          • 37
        • 3
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