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You can just try that out. If it's only one prime factor to the third power, it means the number is either 23, 33, 53, 73, 113 etc.. if you check those, 53 is 125. 113 is already 1331. 73 is 343 and therefore fits the description, so the number you're looking for is 343.

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Q: The prime factorization of a whole number is one factor raised to the third powerthe number is greater than 300 and less than 400what is the number?
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