Question
Find the prime factorization of number 8212890625.
Answer
The prime factorization of 8212890625 is:
$$ 8212890625 = 5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot29\cdot29 $$Which is the same as :
$$ 8212890625 = 5^{10}\cdot29^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 8212890625 can be written as 5 × 1642578125. |
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| 1642578125 can be written as 5 × 328515625. |
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| 328515625 can be written as 5 × 65703125. |
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| 65703125 can be written as 5 × 13140625. |
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| 13140625 can be written as 5 × 2628125. |
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| 2628125 can be written as 5 × 525625. |
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| 525625 can be written as 5 × 105125. |
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| 105125 can be written as 5 × 21025. |
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| 21025 can be written as 5 × 4205. |
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| 4205 can be written as 5 × 841. |
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| 841 can be written as 29 × 29. |
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| The end nodes are the prime factors of the number 8212890625. |
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