# Finding all divisors of a number

• ShayanJ
In summary, there are multiple methods for factoring large numbers, including Pollard's rho algorithm, elliptic curve factoring, and the number field sieves. These methods involve finding prime factors and using them to determine all the divisors of a number. However, finding prime factors can also be done by trial dividing up to the square root of the number, and then only by the primes. Online tools, such as the one provided, can help with this process.
ShayanJ
Gold Member
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

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.

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

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

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

Hi Shyan,

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

Shyan said:
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.

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.

HallsofIvy said:
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 said:
Could you explain the methods you named?

## 1. What is the definition of a divisor?

A divisor is a number that can evenly divide another number without leaving a remainder. For example, the divisors of 12 are 1, 2, 3, 4, 6, and 12.

## 2. How do you find all divisors of a number?

To find all divisors of a number, you can start by dividing the number by 1 and the number itself. Then, continue to divide the number by the remaining numbers between 2 and the number - 1. Any number that divides the original number without a remainder is a divisor.

## 3. What is the largest divisor of a number?

The largest divisor of a number is the number itself. For example, the largest divisor of 20 is 20.

## 4. Can a number have an infinite number of divisors?

No, a number cannot have an infinite number of divisors. Every number has a finite number of divisors, including 1 and the number itself.

## 5. How can finding all divisors of a number be useful in mathematics and science?

Finding all divisors of a number can be useful in mathematics and science for various reasons. In mathematics, it can help in simplifying fractions and finding common factors. In science, it can be used to determine the factors that affect a certain phenomenon or to analyze data sets. It can also be used in cryptography and prime factorization, which are important in computer science and security.

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