Answer
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Work Step by Step
If a positive integer \( n \) has no integer factors in the range from 2 to the square root of \( n \), then it must be a prime number. This is because if \( n \) had any factors other than 1 and itself, at least one of them would have to be less than or equal to the square root of \( n \). Therefore, the absence of such factors implies that \( n \) is only divisible by 1 and itself, making it a prime number.
This tells us that the task of finding the factors of a positive integer becomes simplified when we only need to check for factors up to the square root of that integer. If we find no factors within this range, we can conclude that the integer is prime without needing to check any further.
