Question
Find the prime factorization of number 6482592000.
Answer
The prime factorization of 6482592000 is:
$$ 6482592000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot41\cdot61 $$Which is the same as :
$$ 6482592000 = 2^{8}\cdot3^{4}\cdot5^{3}\cdot41\cdot61 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 6482592000 can be written as 10 × 648259200. |
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| 10 can be written as 2 × 5. |
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| 648259200 can be written as 10 × 64825920. |
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| 10 can be written as 2 × 5. |
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| 64825920 can be written as 10 × 6482592. |
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| 10 can be written as 2 × 5. |
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| 6482592 can be written as 2 × 3241296. |
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| 3241296 can be written as 2 × 1620648. |
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| 1620648 can be written as 2 × 810324. |
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| 810324 can be written as 2 × 405162. |
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| 405162 can be written as 2 × 202581. |
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| 202581 can be written as 3 × 67527. |
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| 67527 can be written as 3 × 22509. |
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| 22509 can be written as 3 × 7503. |
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| 7503 can be written as 3 × 2501. |
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| 2501 can be written as 41 × 61. |
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| The end nodes are the prime factors of the number 6482592000. |
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