Question
Find the prime factorization of number 1470432000.
Answer
The prime factorization of 1470432000 is:
$$ 1470432000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\cdot5\cdot17\cdot17\cdot53 $$Which is the same as :
$$ 1470432000 = 2^{8}\cdot3\cdot5^{3}\cdot17^{2}\cdot53 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 1470432000 can be written as 10 × 147043200. |
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| 10 can be written as 2 × 5. |
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| 147043200 can be written as 10 × 14704320. |
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| 10 can be written as 2 × 5. |
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| 14704320 can be written as 10 × 1470432. |
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| 10 can be written as 2 × 5. |
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| 1470432 can be written as 2 × 735216. |
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| 735216 can be written as 2 × 367608. |
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| 367608 can be written as 2 × 183804. |
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| 183804 can be written as 2 × 91902. |
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| 91902 can be written as 2 × 45951. |
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| 45951 can be written as 3 × 15317. |
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| 15317 can be written as 17 × 901. |
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| 901 can be written as 17 × 53. |
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| The end nodes are the prime factors of the number 1470432000. |
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