Question
Find the prime factorization of number 1215000000.
Answer
The prime factorization of 1215000000 is:
$$ 1215000000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5 $$Which is the same as :
$$ 1215000000 = 2^{6}\cdot3^{5}\cdot5^{7} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 1215000000 can be written as 10 × 121500000. |
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| 10 can be written as 2 × 5. |
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| 121500000 can be written as 10 × 12150000. |
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| 10 can be written as 2 × 5. |
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| 12150000 can be written as 10 × 1215000. |
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| 10 can be written as 2 × 5. |
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| 1215000 can be written as 10 × 121500. |
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| 10 can be written as 2 × 5. |
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| 121500 can be written as 10 × 12150. |
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| 10 can be written as 2 × 5. |
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| 12150 can be written as 10 × 1215. |
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| 10 can be written as 2 × 5. |
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| 1215 can be written as 5 × 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 1215000000. |
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