Question
Find the prime factorization of number 796262400.
Answer
The prime factorization of 796262400 is:
$$ 796262400 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5 $$Which is the same as :
$$ 796262400 = 2^{17}\cdot3^{5}\cdot5^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 796262400 can be written as 10 × 79626240. |
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| 10 can be written as 2 × 5. |
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| 79626240 can be written as 10 × 7962624. |
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| 10 can be written as 2 × 5. |
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| 7962624 can be written as 2 × 3981312. |
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| 3981312 can be written as 2 × 1990656. |
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| 1990656 can be written as 2 × 995328. |
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| 995328 can be written as 2 × 497664. |
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| 497664 can be written as 2 × 248832. |
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| 248832 can be written as 2 × 124416. |
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| 124416 can be written as 2 × 62208. |
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| 62208 can be written as 2 × 31104. |
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| 31104 can be written as 2 × 15552. |
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| 15552 can be written as 2 × 7776. |
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| 7776 can be written as 2 × 3888. |
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| 3888 can be written as 2 × 1944. |
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| 1944 can be written as 2 × 972. |
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| 972 can be written as 2 × 486. |
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| 486 can be written as 2 × 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 796262400. |
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