Question
Find the prime factorization of number 165375.
Answer
The prime factorization of 165375 is:
$$ 165375 = 3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot7\cdot7 $$Which is the same as :
$$ 165375 = 3^{3}\cdot5^{3}\cdot7^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 165375 can be written as 5 × 33075. |
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| 33075 can be written as 5 × 6615. |
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| 6615 can be written as 5 × 1323. |
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| 1323 can be written as 3 × 441. |
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| 441 can be written as 3 × 147. |
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| 147 can be written as 3 × 49. |
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| 49 can be written as 7 × 7. |
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| The end nodes are the prime factors of the number 165375. |
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