Question
Find the prime factorization of number 1632586752.
Answer
The prime factorization of 1632586752 is:
$$ 1632586752 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3 $$Which is the same as :
$$ 1632586752 = 2^{10}\cdot3^{13} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 1632586752 can be written as 2 × 816293376. |
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| 816293376 can be written as 2 × 408146688. |
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| 408146688 can be written as 2 × 204073344. |
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| 204073344 can be written as 2 × 102036672. |
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| 102036672 can be written as 2 × 51018336. |
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| 51018336 can be written as 2 × 25509168. |
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| 25509168 can be written as 2 × 12754584. |
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| 12754584 can be written as 2 × 6377292. |
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| 6377292 can be written as 2 × 3188646. |
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| 3188646 can be written as 2 × 1594323. |
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| 1594323 can be written as 3 × 531441. |
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| 531441 can be written as 3 × 177147. |
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| 177147 can be written as 3 × 59049. |
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| 59049 can be written as 3 × 19683. |
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| 19683 can be written as 3 × 6561. |
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| 6561 can be written as 3 × 2187. |
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| 2187 can be written as 3 × 729. |
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| 729 can be written as 3 × 243. |
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| 243 can be written as 3 × 81. |
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| 81 can be written as 3 × 27. |
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| 27 can be written as 3 × 9. |
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| 9 can be written as 3 × 3. |
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| The end nodes are the prime factors of the number 1632586752. |
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