Question
Find the prime factorization of number 367200.
Answer
The prime factorization of 367200 is:
$$ 367200 = 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot5\cdot5\cdot17 $$Which is the same as :
$$ 367200 = 2^{5}\cdot3^{3}\cdot5^{2}\cdot17 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 367200 can be written as 10 × 36720. |
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| 10 can be written as 2 × 5. |
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| 36720 can be written as 10 × 3672. |
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| 10 can be written as 2 × 5. |
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| 3672 can be written as 2 × 1836. |
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| 1836 can be written as 2 × 918. |
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| 918 can be written as 2 × 459. |
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| 459 can be written as 3 × 153. |
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| 153 can be written as 3 × 51. |
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| 51 can be written as 3 × 17. |
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| The end nodes are the prime factors of the number 367200. |
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