determine whether the following numbers (a)103 (b)299 (c)817 are prime numbers
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if n is a number, then if n is not divisible by n^(1/2) or any number below it
therefore
(a) closest square to 103 is 100 whose sqrt is 10
103 is not divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10
hence it is a prime number
(b) closest square to 299 is 289 whose sqrt is 17
on dividing it with 17 or any no less than 17 we find that 299 is divisible by 13
hence 299 is not prime
(c)
closest square to 817 is 841 whose sqrt is 29
on dividing it with 29 or a number less than 29 we find that it is divisible by 19
therefore 817 is not a prime number
therefore
(a) closest square to 103 is 100 whose sqrt is 10
103 is not divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10
hence it is a prime number
(b) closest square to 299 is 289 whose sqrt is 17
on dividing it with 17 or any no less than 17 we find that 299 is divisible by 13
hence 299 is not prime
(c)
closest square to 817 is 841 whose sqrt is 29
on dividing it with 29 or a number less than 29 we find that it is divisible by 19
therefore 817 is not a prime number
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