im trying to find the prime factors 289.
I can make a factor tree but this number is tricky i cant divide by numbers 2-12
is there a quick way of working out what it can be divided by?
/= and tips
Well, there are a few obvious points. 289 is odd so not divisible by
any even number. It's digits add to 19 which is not divisible by 3 so it is not divisible by any multiple of 3. It's last digit is not 5 or 0 so it is not divisible by any multiple of 5. If it is not divisible by a prime, it is not divisible by any multiple of that prime so you only need to check prime divisors. And, of course, if it is divisible by any number
larger than the square root of 289 the quotient would be less than that square root, which turns out to be exactly 17!
So we are finished: \(\displaystyle 289= 17^2\). That actually was pretty trivial. I don't know why you would call it "tricky". You say "I can't divide by numbers 2-12". I take it that you tried dividing and found it is not divisible by them. But you really only needed to try 2, 3, 5, 7, and 11, the primes less than 12. And the divisor is just the next prime after 13.
The only "tip" necessary is that you only have to try dividing by primes less than or equal to the square root of the number- here, 2, 3, 5, 7, 11, 13, and 17. You just didn't try very hard!
