Question
Find the prime factorization of number 243000000.
Answer
The prime factorization of 243000000 is:
$$ 243000000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5 $$Which is the same as :
$$ 243000000 = 2^{6}\cdot3^{5}\cdot5^{6} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 243000000 can be written as 10 × 24300000. |
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| 10 can be written as 2 × 5. |
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| 24300000 can be written as 10 × 2430000. |
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| 10 can be written as 2 × 5. |
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| 2430000 can be written as 10 × 243000. |
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| 10 can be written as 2 × 5. |
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| 243000 can be written as 10 × 24300. |
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| 10 can be written as 2 × 5. |
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| 24300 can be written as 10 × 2430. |
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| 10 can be written as 2 × 5. |
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| 2430 can be written as 10 × 243. |
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| 10 can be written as 2 × 5. |
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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 243000000. |
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