Question
Find the prime factorization of number 100800000.
Answer
The prime factorization of 100800000 is:
$$ 100800000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot5\cdot5\cdot5\cdot7 $$Which is the same as :
$$ 100800000 = 2^{9}\cdot3^{2}\cdot5^{5}\cdot7 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 100800000 can be written as 10 × 10080000. |
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| 10 can be written as 2 × 5. |
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| 10080000 can be written as 10 × 1008000. |
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| 10 can be written as 2 × 5. |
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| 1008000 can be written as 10 × 100800. |
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| 10 can be written as 2 × 5. |
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| 100800 can be written as 10 × 10080. |
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| 10 can be written as 2 × 5. |
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| 10080 can be written as 10 × 1008. |
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| 10 can be written as 2 × 5. |
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| 1008 can be written as 2 × 504. |
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| 504 can be written as 2 × 252. |
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| 252 can be written as 2 × 126. |
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| 126 can be written as 2 × 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 100800000. |
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