Finding all divisors of a number

[ShayanJ]

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

 

[ShayanJ]

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

 

[ShayanJ]

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]

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]

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.

 

[ShayanJ]

Could you explain the methods you named?

Please!