Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

◀ back to index

Question

Find the prime factorization of number 240000.

Answer

The prime factorization of 240000 is:

$$ 240000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 240000 = 2^{7}\cdot3\cdot5^{4} $$

Explanation

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

240000 can be written as 10 × 24000.
  • 240000
    • 10
    • 24000
10 can be written as 2 × 5.
  • 240000
    • 10
      • 5
      • 2
    • 24000
24000 can be written as 10 × 2400.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
      • 2400
10 can be written as 2 × 5.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
2400 can be written as 10 × 240.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
        • 240
10 can be written as 2 × 5.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
          • 5
          • 2
        • 240
240 can be written as 10 × 24.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
          • 5
          • 2
        • 240
          • 10
          • 24
10 can be written as 2 × 5.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
          • 5
          • 2
        • 240
          • 10
            • 5
            • 2
          • 24
24 can be written as 2 × 12.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
          • 5
          • 2
        • 240
          • 10
            • 5
            • 2
          • 24
            • 2
            • 12
12 can be written as 2 × 6.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
          • 5
          • 2
        • 240
          • 10
            • 5
            • 2
          • 24
            • 2
            • 12
              • 6
              • 2
6 can be written as 2 × 3.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 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 240000.
  • 240000
    • 10
      • 5
      • 2
    • 24000
      • 10
        • 5
        • 2
      • 2400
        • 10
          • 5
          • 2
        • 240
          • 10
            • 5
            • 2
          • 24
            • 2
            • 12
              • 6
                • 2
                • 3
              • 2
This page was created using
Prime factorization calculator