Question
Find the prime factorization of number 1742400.
Answer
The prime factorization of 1742400 is:
$$ 1742400 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot11\cdot11 $$Which is the same as :
$$ 1742400 = 2^{6}\cdot3^{2}\cdot5^{2}\cdot11^{2} $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 1742400 can be written as 10 × 174240. |
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| 10 can be written as 2 × 5. |
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| 174240 can be written as 10 × 17424. |
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| 10 can be written as 2 × 5. |
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| 17424 can be written as 2 × 8712. |
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| 8712 can be written as 2 × 4356. |
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| 4356 can be written as 2 × 2178. |
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| 2178 can be written as 2 × 1089. |
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| 1089 can be written as 3 × 363. |
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| 363 can be written as 3 × 121. |
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| 121 can be written as 11 × 11. |
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| The end nodes are the prime factors of the number 1742400. |
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