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Question

Find the prime factorization of number 19680.

Answer

The prime factorization of 19680 is:

$$ 19680 = 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot41 $$

Which is the same as :

$$ 19680 = 2^{5}\cdot3\cdot5\cdot41 $$

Explanation

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

19680 can be written as 10 × 1968.
  • 19680
    • 10
    • 1968
10 can be written as 2 × 5.
  • 19680
    • 10
      • 5
      • 2
    • 1968
1968 can be written as 2 × 984.
  • 19680
    • 10
      • 5
      • 2
    • 1968
      • 2
      • 984
984 can be written as 2 × 492.
  • 19680
    • 10
      • 5
      • 2
    • 1968
      • 2
      • 984
        • 492
        • 2
492 can be written as 2 × 246.
  • 19680
    • 10
      • 5
      • 2
    • 1968
      • 2
      • 984
        • 492
          • 2
          • 246
        • 2
246 can be written as 2 × 123.
  • 19680
    • 10
      • 5
      • 2
    • 1968
      • 2
      • 984
        • 492
          • 2
          • 246
            • 123
            • 2
        • 2
123 can be written as 3 × 41.
  • 19680
    • 10
      • 5
      • 2
    • 1968
      • 2
      • 984
        • 492
          • 2
          • 246
            • 123
              • 3
              • 41
            • 2
        • 2
The end nodes are the prime factors of the number 19680.
  • 19680
    • 10
      • 5
      • 2
    • 1968
      • 2
      • 984
        • 492
          • 2
          • 246
            • 123
              • 3
              • 41
            • 2
        • 2
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