Finding all divisors of a number

Shyan

Good time people
Is there any way other than dividing the number from 2 to its half to find all of its divisors?
Anyway may help so feel free telling your ideas
thanks

skeptic2

First of all you don't have to divide up to the number's half, only up to it square root. Second, you only have to divide by prime numbers.

CRGreathouse

It's easiest to first find all the prime factors of a number, and then determine the divisors from that list. Finding the prime factors requires only trial dividing up to the square root of the number -- and then only by the primes, if you like.

Methods like Pollard's rho algorithm, elliptic curve factoring, and the number field sieves can be used to factor large numbers (say, > 10^9) much more quickly.

Practically, if you don't recognize these terms, I recommend a tool like
http://www.alpertron.com.ar/ECM.HTM

Shyan

Hello
Did you noticed 71,a prime factor of 284?
it is greater than 16.85 that is the square root of 284.

Shyan

And one more thing...
Could you explain the methods you named?
the page you gave the link of,doesn't include a explanation about the method itself.
I searched it in the internet but i found no easy explanation.
thanks

*Roger09*

Hi Shyan,

I had visited a site called eTutorWorld its online tuition site.

Office_Shredder

Quote by Shyan

Hello
Did you noticed 71,a prime factor of 284?
it is greater than 16.85 that is the square root of 284.

Yes, but 284=71*4. So by finding 4, you've found 71 as a factor also. If a> sqrt(n), and ab = n, then b<sqrt(n) necessarily.

HallsofIvy

Yes, but I think Shyan was referring to Skeptic2's advice to only go up to and only use prime numbers. 2 divides into 284 142 times but you don't immediately see the "71". Of course the intelligent thing to do once you have 284= 142 would be to ignore the 284 and start factoring 142 so that you immediately get 2*71 but it is not clear that was what Skeptic2 meant.

skeptic2

Quote by HallsofIvy

Yes, but I think Shyan was referring to Skeptic2's advice to only go up to and only use prime numbers. 2 divides into 284 142 times but you don't immediately see the "71". Of course the intelligent thing to do once you have 284= 142 would be to ignore the 284 and start factoring 142 so that you immediately get 2*71 but it is not clear that was what Skeptic2 meant.

Agreed.

Shyan

Quote by shyan

Could you explain the methods you named?

Please!

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Shyan	Finding all divisors of a number Tweet Good time people Is there any way other than dividing the number from 2 to its half to find all of its divisors? Anyway may help so feel free telling your ideas thanks

skeptic2	First of all you don't have to divide up to the number's half, only up to it square root. Second, you only have to divide by prime numbers.

Shyan	Finding all divisors of a number Hello Did you noticed 71,a prime factor of 284? it is greater than 16.85 that is the square root of 284.

Roger09	Hi Shyan, I had visited a site called eTutorWorld its online tuition site.

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	Yes, but I think Shyan was referring to Skeptic2's advice to only go up to and only use prime numbers. 2 divides into 284 142 times but you don't immediately see the "71". Of course the intelligent thing to do once you have 284= 142 would be to ignore the 284 and start factoring 142 so that you immediately get 2*71 but it is not clear that was what Skeptic2 meant.