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Question

Find the prime factorization of number 11520.

Answer

The prime factorization of 11520 is:

$$ 11520 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5 $$

Which is the same as :

$$ 11520 = 2^{8}\cdot3^{2}\cdot5 $$

Explanation

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

11520 can be written as 10 × 1152.
  • 11520
    • 10
    • 1152
10 can be written as 2 × 5.
  • 11520
    • 10
      • 5
      • 2
    • 1152
1152 can be written as 2 × 576.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
576 can be written as 2 × 288.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
        • 2
288 can be written as 2 × 144.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
        • 2
144 can be written as 2 × 72.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
            • 72
            • 2
        • 2
72 can be written as 2 × 36.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
            • 72
              • 2
              • 36
            • 2
        • 2
36 can be written as 2 × 18.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
            • 72
              • 2
              • 36
                • 18
                • 2
            • 2
        • 2
18 can be written as 2 × 9.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
            • 72
              • 2
              • 36
                • 18
                  • 2
                  • 9
                • 2
            • 2
        • 2
9 can be written as 3 × 3.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
            • 72
              • 2
              • 36
                • 18
                  • 2
                  • 9
                    • 3
                    • 3
                • 2
            • 2
        • 2
The end nodes are the prime factors of the number 11520.
  • 11520
    • 10
      • 5
      • 2
    • 1152
      • 2
      • 576
        • 288
          • 2
          • 144
            • 72
              • 2
              • 36
                • 18
                  • 2
                  • 9
                    • 3
                    • 3
                • 2
            • 2
        • 2
This page was created using
Prime factorization calculator