Find divisors of a number algorithm software

You can use double precision numbers or numbers converted to symbolic objects. All of the listed numbers are answers that i found p11 n31 p121728 n31728 p9091x3x9x101x303x909 n3909909909. Divisors of a number sum product number of divisors. Also, i am aware that there are much faster algorithms to generate fixed number of prime numbersi am avoiding them until i fully understand the algorithm. Find all divisors of a natural number set 1 geeksforgeeks. If the number is large, use prime factorization, then find all the possible powers that can be made, then you have all the divisors. To find a prime factor, we may recursively factorize the divisor d, run algorithm for d and nd. First of all, your algorithm for primality checking is rather naive and can be optimized in various ways. A naive solution would be to iterate all the numbers from 1 to n, checking if that number divides n and printing it. Heres a c program to print all the divisors of a given number with output and proper explanation.

It may be better to implement a true prime generator, rather than a fixed set, as discussed with examples here, but that was not my immediate concern. Find all divisors of a natural number set 2 geeksforgeeks. How to find all divisors of a number in a very easy way youtube. Apr 21, 2017 i was working on one of the math programming challenges from project euler recently and needed to implement an algorithm to find all of the divisors of a biginteger.

Sum of all proper divisors of natural numbers in an array. In that case, we use a different set of x, y and c and try again. And if the input number is 315, then output should be 3 3 5 7. Create a routine to generate all the proper divisors of a number. This technique uses prime factorization and looking at the exponent permutations. Can you think of a way to find all the divisors of 889, when i gave you the two prime factors. If the number is greater than 45000, check to see if it is divisible by any prime. You check if the number is prime before looking for divisors. Jan 03, 2016 the video explains how to find the divisors of a number efficiently in osqrtn time. However for now thats just me guessing, so you should be more. This program uses two assist macros xdeco, xprnt to keep the code as short as possible.

This function computes and returns the number of divisors an integer has. Find two numbers you can multiply together to get the number, not including 1. How to determine the number of divisors of an integer. If y is the product of two distinct prime numbers, then factors will be 1, both. The integer variable n is the number whose divisors are being calculated and i is the loop variable. I need to find all possible divisors d for a given number n that provide integers in nd. Mathworks is the leading developer of mathematical. What is an efficient algorithm to find divisors of any number. May 22, 2016 how to find all divisors of a number in a very easy way by subhankar bemathematified. If a prime factor p appears e times in the prime factorization of n, then we can use the factor p up to e times in the subset. Program to find count of numbers having odd number of divisors in given range. You dont need to search for both of these, because once youve found that 100 is divisible by 2, you can do 100 2 to find 50, which is the other divisor. What is the best way to get all the divisors of a number. And after working through all the various division methods of locating prime numbers including the basic divide and conquer method to the esieve method, i have developed an algorithm that once having a clear understanding where prime numbers could occur, i can apply the esieve method by addition not by multiplication.

The overall efficiency of this algorithm will depend entirely on the efficiency of the. C program to find sum of proper divisors of number using. By the way, i had to program this myself, if anyone knows of a standard. Find a number in the range 1 to 20,000 with the most proper divisors. Marvin dookharan, software engineer, informal logician, empiricist. Check if a number has prime count of divisors geeksforgeeks.

Efficient program to print all prime factors of a given number. Nov 17, 2011 i need to find all possible divisors d for a given number n that provide integers in nd. I read already know the largest common diviser of 2 numbers and thought his question was bad english leading on from this. You were asked to find the one number with the most divisors only. Divisor of numbers is meant integer that divides the number without a remainder. As this is a logic it can be applied not only in java but other programming languages too for finding the divisors of a given number. How to find all the divisors of any number youtube. How to find all divisors of a number in a very easy way by subhankar bemathematified. Find sum of divisors of all the divisors of a natural number. A proper divisor of a natural number is the divisor that is strictly less than the number.

Find the largest good number in the divisors of given number n. Find n such that pnn3 where pn is a function that multiplies all the factors of that number. But not an efficient method, because it needs more iteration loops. You get all divisors of 889 by taking one of the numbers 1, 7 and multiplying by one of the numbers 1, 127. If you call divisors for a doubleprecision number, then it returns a vector of doubleprecision numbers. Mar 29, 2019 find two numbers you can multiply together to get the number, not including 1. Program to print all the divisors of a given number c. The % symbol is used to find the remainder, the condition here is checked whether the remainder is 0. This will take us to 24, with 8 divisors, 36 with 9, or 60 with 12. As far as efficiency is concerned you should first generate a list of divisors 12 2,2,3 then group them 2,2,3 then apply product of sets see here.

Find the winner of the game based on greater number of divisors. Find sum of inverse of the divisors when sum of divisors and the number is given. Please solve it on practice first, before moving on to the solution. To find the smallest divisor of an integer n is very straight forward. For example, 12 and 2 are factors of 24, so draw a split branch coming down from.

Dmitriy is right that youll want the sieve of atkin to generate the prime list but i dont believe that takes care of the whole issue. Apr 01, 2016 this technique uses prime factorization and looking at the exponent permutations. To make more divisors, we could multiply by 2,3, or 5. Total number of divisors for a given number geeksforgeeks. That does a maximum of about 5000 checks and you dont waste any time checking nonprimes. I personally reinvented and came up with this method for a. When referred to as the divisor function, it counts the number of divisors of an integer including 1 and the number itself. Given a natural number n, print all distinct divisors of it.

The naive approach count the number of divisors for each n in the given range. Find the number of divisors of all numbers in the range 1, n find if given number is sum of first n natural numbers. The algorithm ive used is the same i have described. So youre basically calculating the sum from 0 to idx for each idx from 0 to n. The following is a c program to find the number of divisors of a given number. Inside the loop, we are checking if the number n is divisible by the. The video explains how to find the divisors of a number efficiently in osqrtn time. Given a number n, write an efficient function to print all prime factors of n. The problem is to find all divisors of a given integer n. Given a natural number, calculate sum of all its proper divisors. But it is very slow and i believe it can be optimized for speed. A divisor, also known as a factor, is an integer m which evenly divides n. Querying maximum number of divisors that a number in a given range has. Check if a number is divisible by all prime divisors of another number.

Already know the largest common diviser of 2 numbers, but i cannot find anything considering the second largest divisor of a number. Find divisors of a number, efficiently osqrtn youtube. A divisor is a number that divides another number completely. Finding divisors of a number with python alexwlchan. If we take into account that all numbers divisible by 2 cant be primes, we can speed this up as well by starting the fomrer loop at 3 and only check each second number. Just take the numbers 2, 3, 4,n and divide n with each of number in ascending order. Please read this article to find the count of divisors of a number. In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.

Find maximum divisors of a number in range mathematics. Mar 24, 20 the % symbol is used to find the remainder, the condition here is checked whether the remainder is 0. Find all numbers such that product of all divisorscube. What is the formula for finding out the total number of. So for every divisor you find, use division to find its partner at the same time. Find all numbers such that product of all divisorscube of. Using this method you can get the divisors of even very large numbers relatively qu. The algorithm works in the sense that it finds all the prime factors, but not all the factors i.

Dec, 2016 to find the smallest divisor of an integer n is very straight forward. For example, the divisors of 12 are 1, 2, 3, 4, 6 and 12. Show the number and just the count of how many proper divisors it. Hello, i need to find all possible divisors d for a given number n that provide integers in nd. Nobody asked you to find the numbers of divisors of all numbers. Note that this problem is different from finding all prime factors. It appears in a number of remarkable identities, including relationships on the riemann zeta function and the eisenstein series of. Algorithm to find all divisors of biginteger sjgp software. You can use an algorithm where you try all possible exponents for 2 that could lead to the smallest number with n divisors, then all possible exponents for 3, and so on. Using this fact we could speed up our program significantly. How to find the maximum number of divisors of a number. Yes medalgod i also assumed it but the question of the op was. A bad bruteforce approach would be to visit all values from 1 to n and see which ones divide evenly into n.

Show the number and just the count of how many proper divisors it has. Algorithm to calculate the number of divisors of a given number. Algorithm to calculate the number of divisors of a given. How to find all divisors of a number in a very easy way. More importantly, this is an optimization only if the argument is prime, but is counterproductive in the vast majority of cases when it isnt prime. Draw a split branch coming down from the original number, and write the two factors below it. The algorithm may not find the factors and return a failure for composite n. We, however have to careful if there are two equal divisors as in case of 10, 10.

This algorithm will work correctly for the number which are perfect square as well as the numbers which are not perfect square. So find the maximum value of i for every prime divisor p such that n % p i 0. Find divisors for a given number matlab answers matlab. I have studied prime number properties for almost 20 years. Nov 17, 2016 this feature is not available right now.