Question
Find the prime factorization of number 176400.
Answer
The prime factorization of 176400 is:
$$ 176400 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot7\cdot7 $$Which is the same as :
$$ 176400 = 2^{4}\cdot3^{2}\cdot5^{2}\cdot7^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 176400 can be written as 10 × 17640. |
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| 10 can be written as 2 × 5. |
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| 17640 can be written as 10 × 1764. |
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| 10 can be written as 2 × 5. |
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| 1764 can be written as 2 × 882. |
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| 882 can be written as 2 × 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 176400. |
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