Question
Find the prime factorization of number 162000.
Answer
The prime factorization of 162000 is:
$$ 162000 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5 $$Which is the same as :
$$ 162000 = 2^{4}\cdot3^{4}\cdot5^{3} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 162000 can be written as 10 × 16200. |
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| 10 can be written as 2 × 5. |
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| 16200 can be written as 10 × 1620. |
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| 10 can be written as 2 × 5. |
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| 1620 can be written as 10 × 162. |
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| 10 can be written as 2 × 5. |
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| 162 can be written as 2 × 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 162000. |
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