Question
Find the prime factorization of number 15142400.
Answer
The prime factorization of 15142400 is:
$$ 15142400 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot7\cdot13\cdot13 $$Which is the same as :
$$ 15142400 = 2^{9}\cdot5^{2}\cdot7\cdot13^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 15142400 can be written as 10 × 1514240. |
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| 10 can be written as 2 × 5. |
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| 1514240 can be written as 10 × 151424. |
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| 10 can be written as 2 × 5. |
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| 151424 can be written as 2 × 75712. |
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| 75712 can be written as 2 × 37856. |
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| 37856 can be written as 2 × 18928. |
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| 18928 can be written as 2 × 9464. |
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| 9464 can be written as 2 × 4732. |
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| 4732 can be written as 2 × 2366. |
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| 2366 can be written as 2 × 1183. |
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| 1183 can be written as 7 × 169. |
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| 169 can be written as 13 × 13. |
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| The end nodes are the prime factors of the number 15142400. |
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