Question
Find the prime factorization of number 4084101000.
Answer
The prime factorization of 4084101000 is:
$$ 4084101000 = 2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot7\cdot7\cdot7\cdot7\cdot7 $$Which is the same as :
$$ 4084101000 = 2^{3}\cdot3^{5}\cdot5^{3}\cdot7^{5} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 4084101000 can be written as 10 × 408410100. |
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| 10 can be written as 2 × 5. |
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| 408410100 can be written as 10 × 40841010. |
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| 10 can be written as 2 × 5. |
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| 40841010 can be written as 10 × 4084101. |
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| 10 can be written as 2 × 5. |
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| 4084101 can be written as 3 × 1361367. |
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| 1361367 can be written as 3 × 453789. |
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| 453789 can be written as 3 × 151263. |
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| 151263 can be written as 3 × 50421. |
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| 50421 can be written as 3 × 16807. |
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| 16807 can be written as 7 × 2401. |
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| 2401 can be written as 7 × 343. |
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| 343 can be written as 7 × 49. |
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| 49 can be written as 7 × 7. |
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| The end nodes are the prime factors of the number 4084101000. |
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