Question
Find the prime factorization of number 387072.
Answer
The prime factorization of 387072 is:
$$ 387072 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot7 $$Which is the same as :
$$ 387072 = 2^{11}\cdot3^{3}\cdot7 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 387072 can be written as 2 × 193536. |
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| 193536 can be written as 2 × 96768. |
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| 96768 can be written as 2 × 48384. |
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| 48384 can be written as 2 × 24192. |
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| 24192 can be written as 2 × 12096. |
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| 12096 can be written as 2 × 6048. |
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| 6048 can be written as 2 × 3024. |
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| 3024 can be written as 2 × 1512. |
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| 1512 can be written as 2 × 756. |
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| 756 can be written as 2 × 378. |
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| 378 can be written as 2 × 189. |
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| 189 can be written as 3 × 63. |
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| 63 can be written as 3 × 21. |
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| 21 can be written as 3 × 7. |
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| The end nodes are the prime factors of the number 387072. |
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