Question
Find the prime factorization of number 258280326.
Answer
The prime factorization of 258280326 is:
$$ 258280326 = 2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3 $$Which is the same as :
$$ 258280326 = 2\cdot3^{17} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 258280326 can be written as 2 × 129140163. |
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| 129140163 can be written as 3 × 43046721. |
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| 43046721 can be written as 3 × 14348907. |
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| 14348907 can be written as 3 × 4782969. |
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| 4782969 can be written as 3 × 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 258280326. |
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