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Prime Number

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Prime Number

by rainmaker » Mon Feb 08, 2010 10:21 am
Hi all,

What is the fastest way to determine if a number is prime? I see some questions in which you need to check if a number is prime or not. The problem is sometimes the number is a huge number.

Thanks
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by harsh.champ » Mon Feb 08, 2010 10:49 am
rainmaker wrote:Hi all,

What is the fastest way to determine if a number is prime? I see some questions in which you need to check if a number is prime or not. The problem is sometimes the number is a huge number.

Thanks
Basically,you have to memorize some divisibility rules of prime no.s .
1:check if even or not.[divisible by 2]
2:check if sum of digits is divisible by 3. [ divisible by 3]
3:check if the no. ends with a 5 or 0. [divisible by 5]

Similarly,you have to remember the rules for 7,11,13,17,19 which can be quite complicated.

I think this link will help you:- https://en.wikipedia.org/wiki/Divisibility_rule
Just keep in mind that you learn them.
[Personally I don't think you will need to know for above than 19 e.g:-23,29 etc.]

Further ,if you have any doubt you can post in this thread afterwards.

:P
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by money9111 » Mon Feb 08, 2010 12:56 pm
yeah the divisibilities rules come in handy when trying to figure this out. if you memorize them, you'll be able to tell quite quickly whether or not a number is prime... MGMAT number properties book will serve you well because it speaks to other cases where knowing primes/divisibility rules are helpful
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by jeffedwards » Mon Feb 08, 2010 5:46 pm
I found a good one from the study cards that used to be free on this site. Basically what it says is

"¢ You start with the smallest prime number and see if it's a factor.
"¢ You continue until you find a number that's a factor (in which case it's not a prime), or you reach a prime number that is ≥ the square root of the number you are testing (in which case it is a prime)

Additionally, I found a great link (https://bit.ly/blmqtA) to quickly figure out square roots

I memorized the first 100; that has helped with most problems.
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by money9111 » Mon Feb 08, 2010 8:55 pm
jeffedwards I'm not seeing where the squares are listed in the link you gave... where should I click?
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by thephoenix » Tue Feb 09, 2010 2:27 am
rainmaker wrote:Hi all,

What is the fastest way to determine if a number is prime? I see some questions in which you need to check if a number is prime or not. The problem is sometimes the number is a huge number.

Thanks
for GMAT quickest way is tofind the nearest square root of the no. and then check div by all prime no's less than the square root of the number

in GMAT u will get more than 2 digit no.
for eg to check for 79
9^2=81 and 8^2=64
hence we need to check whether 79 is div by2,3,5,7 if yes than its not a prime no if no than its a prime no.
here its not and hence its a prime no...

HTH
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by jeffedwards » Tue Feb 09, 2010 8:32 am
money9111 wrote:jeffedwards I'm not seeing where the squares are listed in the link you gave... where should I click?
Sorry, I may not have been clear. It's not a list, the article just explains another method to find the square root of a number. I thought it was a nice little trick.
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by rainmaker » Tue Feb 09, 2010 9:57 am
Thanks Guys!

Jeff, thanks for the link.
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by money9111 » Wed Feb 10, 2010 12:10 pm
jeffedwards - aaahhh ok i get it now... thanks

thephoenix - thank you for the explanation! gotta remember this... therefore it's going in my notecards
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by djkvakin » Thu Feb 11, 2010 3:04 pm
Here is a quick way to see if the number is divisible by 7:
To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number.
Example: If you had 203, you would double the last digit to get six, and subtract that from 20 to get 14. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again.
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by djkvakin » Thu Feb 11, 2010 3:11 pm
Great link!
https://mathforum.org/k12/mathtips/division.tips.html
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by harsh.champ » Thu Feb 18, 2010 10:54 am
Thanks djkvakin for the link.
The link in wikipedia(given by me above) only lists the division methods and where you can memorize them.
Over here ,the explanation is given in details by Dr.Rob,Sara and many others which helps us to strengthen our concepts.
Though I would say for the exam-day it is better only to learn a few divisibility rules as going too much in-depth can get confusing as we also have numerous geometry properties to remember.What-say??

For understanding purposes,no doubt that the link is very beneficial.
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by ajith » Thu Feb 18, 2010 1:17 pm
harsh.champ wrote:
Thanks djkvakin for the link.
The link in wikipedia(given by me above) only lists the division methods and where you can memorize them.
Over here ,the explanation is given in details by Dr.Rob,Sara and many others which helps us to strengthen our concepts.
Though I would say for the exam-day it is better only to learn a few divisibility rules as going too much in-depth can get confusing as we also have numerous geometry properties to remember.What-say??

For understanding purposes,no doubt that the link is very beneficial.
Well Depends on your brain's capacity. Whatever works fine with you do that, if you can remember 100 numbers with no pattern it works well. If you can master Eratosthenes Sieve do that. If you are good at division go upto sqrt of n and check that. If you say divisibility rules help, probably try that out. Some people may like Vedic maths and it would help.

I would say whatever suits you do that but, never ever try to cheat.
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by shashank.ism » Fri Feb 19, 2010 2:24 am
Well overall it comes to memorizing which will help you in real exam. If you need outside exam or to make a sheet of all the prime numbers. Just try my small programming you can check any number whether its prime or not..
https://shashankmadhukar.byethost5.com/t ... umber.html
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