Question
Find the prime factorization of number 1254400.
Answer
The prime factorization of 1254400 is:
$$ 1254400 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot7\cdot7 $$Which is the same as :
$$ 1254400 = 2^{10}\cdot5^{2}\cdot7^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 1254400 can be written as 10 × 125440. |
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| 10 can be written as 2 × 5. |
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| 125440 can be written as 10 × 12544. |
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| 10 can be written as 2 × 5. |
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| 12544 can be written as 2 × 6272. |
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| 6272 can be written as 2 × 3136. |
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| 3136 can be written as 2 × 1568. |
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| 1568 can be written as 2 × 784. |
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| 784 can be written as 2 × 392. |
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| 392 can be written as 2 × 196. |
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| 196 can be written as 2 × 98. |
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| 98 can be written as 2 × 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 1254400. |
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