Question
Find the prime factorization of number 74688000.
Answer
The prime factorization of 74688000 is:
$$ 74688000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\cdot5\cdot389 $$Which is the same as :
$$ 74688000 = 2^{9}\cdot3\cdot5^{3}\cdot389 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 74688000 can be written as 10 × 7468800. |
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| 10 can be written as 2 × 5. |
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| 7468800 can be written as 10 × 746880. |
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| 10 can be written as 2 × 5. |
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| 746880 can be written as 10 × 74688. |
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| 10 can be written as 2 × 5. |
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| 74688 can be written as 2 × 37344. |
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| 37344 can be written as 2 × 18672. |
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| 18672 can be written as 2 × 9336. |
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| 9336 can be written as 2 × 4668. |
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| 4668 can be written as 2 × 2334. |
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| 2334 can be written as 2 × 1167. |
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| 1167 can be written as 3 × 389. |
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| The end nodes are the prime factors of the number 74688000. |
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