The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56,
For the record, system. See my post below.
By the way, I really like this algorithm. I've fixed the code, and I'm confident that it now works as it should.
Also, when I comment the bottom function call out, it still seems to work. I'd intended to make a vector or integers having the 'L' suffix everywherebut must have gotten bored typing part way through.
In addition to the original links, this paper along with this post from primo were very helpful for this last stage many kudos to primo. Primo does a great job of explaining the guts of the QS in a relatively short space and also wrote a pretty amazing algorithm it will factor the number at the bottom, 38!
As promised, below is my humble R implementation of the Quadratic Sieve. I have been working on this algorithm sporadically since I promised it in late January. I will not try to explain it fully unless requested This has proved to be one of the most challenging algorithms I have ever attempted to execute as it is demanding both from a programmer's point of view as well as mathematically.
This algorithm, as it stands, does not serve very well as a general prime factorization algorithm. If it was optimized further, it would need to be accompanied by a section of code that factors out smaller primes i.
I know the OP was looking for a method to return all factors and not the prime factorization, but this algorithm if optimized further coupled with one of the algorithms above would be a force to reckon with as a general factoring algorithm especially given that the OP was needing something for Project Eulerwhich usually requires much more than brute force methods.
Dontas appeared on a while back Kudos on that as well. The number n5 above is a very interesting number.
Check it out here The Breaking Point!!!! It should be noted that the QS generally doesn't perform as well as the Pollard's rho algorithm on smaller numbers and the power of the QS starts to become apparent as the numbers get larger.
Anywho, as always, I hope this inspires somebody!The factors of 28 are: 1,2,4,7,14 and Rember, the factors of 28 are all of the natural numbers which divide into 28, with no remainder. 42/21 = 2 gives remainder 0 and so are divisible by 21 42/42 = 1 gives remainder 0 and so are divisible by We get factors of 42 numbers by finding numbers that can divide 42 without remainder or alternatively numbers that can multiply together to equal the target number being converted.
[Solved] What are the factors of 42? The factors are.
Factoring a number means taking the number apart to find its factors--it's like multiplying in reverse. Here are lists of all the factors of 16, 20, and 16 --> 1, 2, 4, 8, What Are the Factors of 30? The factors of 30 are 1, 2, 3, 5, 6, 10, 15, Calcating the factors of 30 is straightforward.
First, every number is divisible by. Use this prime numbers calculator to find all prime factors of a given integer number up to 1 trillion. This calculator presents: Factorization in a prime factors tree; For the first prime numbers, this calculator indicates the index of the prime number. The n th prime number is denoted as Prime[n].