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- anonymous

If you want to examine if a integer is a prime number can you try with dividing it by
the prime numbers 2 , 3, 5 etc . What is the largest prime number that there is reason to try ?
Determine if any of the numbers 171, 203 , 211, 567 or 7669 is prime and factorize them otherwise.

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- IrishBoy123

the number's square root is a cut off point

- welshfella

A short cut to see if a number is divisible 3 is to add the digits up until you have 1 didigte
If this digit is 3 , 6 or 9 then t is divisible by 3.

- welshfella

so from this you can see that 171 and 567 are not prime

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- welshfella

square root of 203 is 14.25 so you keep dividing by prime numbers up to and including 13.

- zzr0ck3r

It is sort of fun to think about why the square root thing works.

- anonymous

@@zzr0ck3r could you explain why that works? is it because everything after the squareroot is like testing the dividers all over again?

- welshfella

I think it works because if there is an integer quotient you would have found it already when dividing by the lower primes.

- welshfella

- yes - it is like testing the dividers all over again

- imqwerty

well lets take any number say x
the biggest factor of any number can be the square root of the number itself :) when u prime factorize x u will get prime numbers as its factors
so the prime factors of any number x are always smaller than or equal to root{x}
if x is a prime number then there will be no factors but if x is composite then the factors it will have will always be less than or equal to root(x)
so to check if x is prime we find root x nd then try dividing x by all prime numbers less then rootx

- anonymous

so if Im gonna see if 7669 is a prime, how do i do? the sqrt of 7669 is 87.6, then still I gotta know the primes upp to that

- anonymous

- zzr0ck3r

yes

- welshfella

yes 2,3,5,7 etc

- anonymous

up to 83

- welshfella

thats correct
because square root of 7669 is 87.57

- welshfella

oh you found that already - sorry

- welshfella

is 211 a prime?

- anonymous

no, 3*3*19

- welshfella

that is 171

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