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Question

Find the prime factorization of number 1440.

Answer

The prime factorization of 1440 is:

$$ 1440 = 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5 $$

Which is the same as :

$$ 1440 = 2^{5}\cdot3^{2}\cdot5 $$

Explanation

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

1440 can be written as 10 × 144.
  • 1440
    • 10
    • 144
10 can be written as 2 × 5.
  • 1440
    • 10
      • 5
      • 2
    • 144
144 can be written as 2 × 72.
  • 1440
    • 10
      • 5
      • 2
    • 144
      • 2
      • 72
72 can be written as 2 × 36.
  • 1440
    • 10
      • 5
      • 2
    • 144
      • 2
      • 72
        • 36
        • 2
36 can be written as 2 × 18.
  • 1440
    • 10
      • 5
      • 2
    • 144
      • 2
      • 72
        • 36
          • 2
          • 18
        • 2
18 can be written as 2 × 9.
  • 1440
    • 10
      • 5
      • 2
    • 144
      • 2
      • 72
        • 36
          • 2
          • 18
            • 9
            • 2
        • 2
9 can be written as 3 × 3.
  • 1440
    • 10
      • 5
      • 2
    • 144
      • 2
      • 72
        • 36
          • 2
          • 18
            • 9
              • 3
              • 3
            • 2
        • 2
The end nodes are the prime factors of the number 1440.
  • 1440
    • 10
      • 5
      • 2
    • 144
      • 2
      • 72
        • 36
          • 2
          • 18
            • 9
              • 3
              • 3
            • 2
        • 2
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Prime factorization calculator