Question
Find the prime factorization of number 25401600.
Answer
The prime factorization of 25401600 is:
$$ 25401600 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot7\cdot7 $$Which is the same as :
$$ 25401600 = 2^{8}\cdot3^{4}\cdot5^{2}\cdot7^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 25401600 can be written as 10 × 2540160. |
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| 10 can be written as 2 × 5. |
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| 2540160 can be written as 10 × 254016. |
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| 10 can be written as 2 × 5. |
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| 254016 can be written as 2 × 127008. |
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| 127008 can be written as 2 × 63504. |
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| 63504 can be written as 2 × 31752. |
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| 31752 can be written as 2 × 15876. |
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| 15876 can be written as 2 × 7938. |
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| 7938 can be written as 2 × 3969. |
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| 3969 can be written as 3 × 1323. |
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| 1323 can be written as 3 × 441. |
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| 441 can be written as 3 × 147. |
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| 147 can be written as 3 × 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 25401600. |
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