Question
Find the prime factorization of number 75600.
Answer
The prime factorization of 75600 is:
$$ 75600 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot5\cdot5\cdot7 $$Which is the same as :
$$ 75600 = 2^{4}\cdot3^{3}\cdot5^{2}\cdot7 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 75600 can be written as 10 × 7560. |
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| 10 can be written as 2 × 5. |
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| 7560 can be written as 10 × 756. |
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| 10 can be written as 2 × 5. |
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| 756 can be written as 2 × 378. |
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| 378 can be written as 2 × 189. |
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| 189 can be written as 3 × 63. |
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| 63 can be written as 3 × 21. |
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| 21 can be written as 3 × 7. |
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| The end nodes are the prime factors of the number 75600. |
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