Find the prime factorization of number 46656.
Answer
The prime factorization of 46656 is:
$$ 46656 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3 $$Which is the same as :
$$ 46656 = 2^{6}\cdot3^{6} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 46656 can be written as 2 × 23328. |
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| 23328 can be written as 2 × 11664. |
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| 11664 can be written as 2 × 5832. |
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| 5832 can be written as 2 × 2916. |
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| 2916 can be written as 2 × 1458. |
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| 1458 can be written as 2 × 729. |
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| 729 can be written as 3 × 243. |
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| 243 can be written as 3 × 81. |
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| 81 can be written as 3 × 27. |
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| 27 can be written as 3 × 9. |
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| 9 can be written as 3 × 3. |
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| The end nodes are the prime factors of the number 46656. |
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