Question
Find the prime factorization of number 1296000.
Answer
The prime factorization of 1296000 is:
$$ 1296000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5 $$Which is the same as :
$$ 1296000 = 2^{7}\cdot3^{4}\cdot5^{3} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 1296000 can be written as 10 × 129600. |
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| 10 can be written as 2 × 5. |
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| 129600 can be written as 10 × 12960. |
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| 10 can be written as 2 × 5. |
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| 12960 can be written as 10 × 1296. |
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| 10 can be written as 2 × 5. |
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| 1296 can be written as 2 × 648. |
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| 648 can be written as 2 × 324. |
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| 324 can be written as 2 × 162. |
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| 162 can be written as 2 × 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 1296000. |
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