Question
Find the prime factorization of number 6616209600.
Answer
The prime factorization of 6616209600 is:
$$ 6616209600 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot7\cdot11\cdot13\cdot17 $$Which is the same as :
$$ 6616209600 = 2^{6}\cdot3^{5}\cdot5^{2}\cdot7\cdot11\cdot13\cdot17 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 6616209600 can be written as 10 × 661620960. |
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| 10 can be written as 2 × 5. |
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| 661620960 can be written as 10 × 66162096. |
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| 10 can be written as 2 × 5. |
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| 66162096 can be written as 2 × 33081048. |
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| 33081048 can be written as 2 × 16540524. |
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| 16540524 can be written as 2 × 8270262. |
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| 8270262 can be written as 2 × 4135131. |
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| 4135131 can be written as 3 × 1378377. |
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| 1378377 can be written as 3 × 459459. |
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| 459459 can be written as 3 × 153153. |
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| 153153 can be written as 3 × 51051. |
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| 51051 can be written as 3 × 17017. |
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| 17017 can be written as 7 × 2431. |
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| 2431 can be written as 11 × 221. |
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| 221 can be written as 13 × 17. |
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| The end nodes are the prime factors of the number 6616209600. |
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