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Find the prime factorization of number 2400.

Answer

The prime factorization of 2400 is:

$$ 2400 = 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5 $$

Which is the same as :

$$ 2400 = 2^{5}\cdot3\cdot5^{2} $$

Explanation

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

2400 can be written as 10 × 240.
  • 2400
    • 10
    • 240
10 can be written as 2 × 5.
  • 2400
    • 10
      • 5
      • 2
    • 240
240 can be written as 10 × 24.
  • 2400
    • 10
      • 5
      • 2
    • 240
      • 10
      • 24
10 can be written as 2 × 5.
  • 2400
    • 10
      • 5
      • 2
    • 240
      • 10
        • 5
        • 2
      • 24
24 can be written as 2 × 12.
  • 2400
    • 10
      • 5
      • 2
    • 240
      • 10
        • 5
        • 2
      • 24
        • 2
        • 12
12 can be written as 2 × 6.
  • 2400
    • 10
      • 5
      • 2
    • 240
      • 10
        • 5
        • 2
      • 24
        • 2
        • 12
          • 6
          • 2
6 can be written as 2 × 3.
  • 2400
    • 10
      • 5
      • 2
    • 240
      • 10
        • 5
        • 2
      • 24
        • 2
        • 12
          • 6
            • 2
            • 3
          • 2
The end nodes are the prime factors of the number 2400.
  • 2400
    • 10
      • 5
      • 2
    • 240
      • 10
        • 5
        • 2
      • 24
        • 2
        • 12
          • 6
            • 2
            • 3
          • 2
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Prime factorization calculator