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Question

Find the prime factorization of number 1120.

Answer

The prime factorization of 1120 is:

$$ 1120 = 2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot7 $$

Which is the same as :

$$ 1120 = 2^{5}\cdot5\cdot7 $$

Explanation

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

1120 can be written as 10 × 112.
  • 1120
    • 10
    • 112
10 can be written as 2 × 5.
  • 1120
    • 10
      • 5
      • 2
    • 112
112 can be written as 2 × 56.
  • 1120
    • 10
      • 5
      • 2
    • 112
      • 2
      • 56
56 can be written as 2 × 28.
  • 1120
    • 10
      • 5
      • 2
    • 112
      • 2
      • 56
        • 28
        • 2
28 can be written as 2 × 14.
  • 1120
    • 10
      • 5
      • 2
    • 112
      • 2
      • 56
        • 28
          • 2
          • 14
        • 2
14 can be written as 2 × 7.
  • 1120
    • 10
      • 5
      • 2
    • 112
      • 2
      • 56
        • 28
          • 2
          • 14
            • 7
            • 2
        • 2
The end nodes are the prime factors of the number 1120.
  • 1120
    • 10
      • 5
      • 2
    • 112
      • 2
      • 56
        • 28
          • 2
          • 14
            • 7
            • 2
        • 2
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Prime factorization calculator