Question
Find the prime factorization of number 4406400.
Answer
The prime factorization of 4406400 is:
$$ 4406400 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot17 $$Which is the same as :
$$ 4406400 = 2^{7}\cdot3^{4}\cdot5^{2}\cdot17 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 4406400 can be written as 10 × 440640. |
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| 10 can be written as 2 × 5. |
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| 440640 can be written as 10 × 44064. |
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| 10 can be written as 2 × 5. |
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| 44064 can be written as 2 × 22032. |
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| 22032 can be written as 2 × 11016. |
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| 11016 can be written as 2 × 5508. |
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| 5508 can be written as 2 × 2754. |
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| 2754 can be written as 2 × 1377. |
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| 1377 can be written as 3 × 459. |
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| 459 can be written as 3 × 153. |
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| 153 can be written as 3 × 51. |
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| 51 can be written as 3 × 17. |
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| The end nodes are the prime factors of the number 4406400. |
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