Question
Find the prime factorization of number 39916800.
Answer
The prime factorization of 39916800 is:
$$ 39916800 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot7\cdot11 $$Which is the same as :
$$ 39916800 = 2^{8}\cdot3^{4}\cdot5^{2}\cdot7\cdot11 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 39916800 can be written as 10 × 3991680. |
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| 10 can be written as 2 × 5. |
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| 3991680 can be written as 10 × 399168. |
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| 10 can be written as 2 × 5. |
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| 399168 can be written as 2 × 199584. |
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| 199584 can be written as 2 × 99792. |
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| 99792 can be written as 2 × 49896. |
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| 49896 can be written as 2 × 24948. |
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| 24948 can be written as 2 × 12474. |
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| 12474 can be written as 2 × 6237. |
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| 6237 can be written as 3 × 2079. |
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| 2079 can be written as 3 × 693. |
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| 693 can be written as 3 × 231. |
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| 231 can be written as 3 × 77. |
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| 77 can be written as 7 × 11. |
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| The end nodes are the prime factors of the number 39916800. |
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