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Question

Find the prime factorization of number 1680.

Answer

The prime factorization of 1680 is:

$$ 1680 = 2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot7 $$

Which is the same as :

$$ 1680 = 2^{4}\cdot3\cdot5\cdot7 $$

Explanation

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

1680 can be written as 10 × 168.
  • 1680
    • 10
    • 168
10 can be written as 2 × 5.
  • 1680
    • 10
      • 5
      • 2
    • 168
168 can be written as 2 × 84.
  • 1680
    • 10
      • 5
      • 2
    • 168
      • 2
      • 84
84 can be written as 2 × 42.
  • 1680
    • 10
      • 5
      • 2
    • 168
      • 2
      • 84
        • 42
        • 2
42 can be written as 2 × 21.
  • 1680
    • 10
      • 5
      • 2
    • 168
      • 2
      • 84
        • 42
          • 2
          • 21
        • 2
21 can be written as 3 × 7.
  • 1680
    • 10
      • 5
      • 2
    • 168
      • 2
      • 84
        • 42
          • 2
          • 21
            • 7
            • 3
        • 2
The end nodes are the prime factors of the number 1680.
  • 1680
    • 10
      • 5
      • 2
    • 168
      • 2
      • 84
        • 42
          • 2
          • 21
            • 7
            • 3
        • 2
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Prime factorization calculator