prime-factoring

I am looking for an optimum way to create a table from n elements so that ideally there are no empty cells, but at the same time the proportion of the table dimensions columns / rows becomes as close to 1 as possible. Of course if n is a square number it is easy since then cols = rows = sqrt( n ); If n is a prime number it is also clear that there will be empty cells, so my current way to handle this is: rows = floor( sqrt(n) ); cols = ceil( n / rows ); For all other cases my plan is to get the prime factors of n and then search all possible permutations for those whose combination has

I wrote the following program to prime factorize a number: import math def prime_factorize(x,li=[]): until = int(math.sqrt(x))+1 for i in xrange(2,until): if not x%i: li.append(i) break else: #This else belongs to for li.append(x) print li #First print statement; This is what is returned return li prime_factorize(x/i,li) if __name__=='__main__': print prime_factorize(300) #Second print statement, WTF. why is this None Following is the output I get: [2, 2, 3, 5, 5] None Altho', the returned value is printed properly, the after returned value seems to be printing none, all the time. What am I

Regular numbers are numbers that evenly divide powers of 60. As an example, 60 2 = 3600 = 48 × 75, so both 48 and 75 are divisors of a power of 60. Thus, they are also regular numbers. This is an extension of rounding up to the next power of two . I have an integer value N which may contain large prime factors and I want to round it up to a number composed of only small prime factors (2, 3 and 5) Examples: f(18) == 18 == 2 1 * 3 2 f(19) == 20 == 2 2 * 5 1 f(257) == 270 == 2 1 * 3 3 * 5 1 What would be an efficient way to find the smallest number satisfying this requirement? The values involved

I need to find out the prime factors of over 300 billion. I have a function that is adding to the list of them...very slowly! It has been running for about an hour now and i think its got a fair distance to go still. Am i doing it completly wrong or is this expected? Edit: Im trying to find the largest prime factor of the number 600851475143. Edit: Result: { List<Int64> ListOfPrimeFactors = new List<Int64>(); Int64 Number = 600851475143; Int64 DividingNumber = 2; while (DividingNumber < Number / DividingNumber) { if (Number % DividingNumber == 0) { ListOfPrimeFactors.Add(DividingNumber);

#include <iostream> using namespace std; void whosprime(long long x) { bool imPrime = true; for(int i = 1; i <= x; i++) { for(int z = 2; z <= x; z++) { if((i != z) && (i%z == 0)) { imPrime = false; break; } } if(imPrime && x%i == 0) cout << i << endl; imPrime = true; } } int main() { long long r = 600851475143LL; whosprime(r); } I'm trying to find the prime factors of the number 600851475143 specified by Problem 3 on Project Euler (it asks for the highest prime factor, but I want to find all of them). However, when I try to run this program I don't get any results. Does it have to do with how