Which of these numbers is prime? Explain why or why not.
407
409
411
413
http://en.wikipedia.org/wiki/Prime_number
So ... which of these can be divided evenly only by itself and 1?
??
Which one(s) are evenly divisible by prime numbers less than the sqrt of the number. The square root of the largest is 20.32. Since they are all odd, 2 is not a divisor, Therefore, division by 3, 7, 11, 13, and 19 are the only tests.
To determine if a number is prime, we need to check if it is divisible by any numbers other than 1 and itself. Let's evaluate each of the given numbers:
407: To check if 407 is prime, we need to find its factors. We can start by checking if it is divisible by any numbers from 2 to the square root of 407 (approximately 20). If there is any number that evenly divides 407, then 407 is not prime. In this case, 407 is divisible by 11, so it is not a prime number.
409: Similar to the previous method, we check if 409 is divisible by any numbers from 2 to the square root of 409 (approximately 20.22). Since there are no numbers other than 1 and itself that divide 409 evenly, it is a prime number.
411: We apply the same process as before and test if 411 is divisible by any numbers from 2 to the square root of 411 (approximately 20.27). Since 411 is divisible by 3, it is not a prime number.
413: Again, we check if 413 is divisible by any numbers from 2 to the square root of 413 (approximately 20.32). As it is divisible by 7, 413 is not a prime number.
In summary, out of the given numbers, only 409 is prime.