How to find divisors of a number in python. You need a better algorithm to find the factors.

How to find divisors of a number in python Aug 23, 2010 · First thought you can find the smallest divisor d (not equal to 1 of course), then N/d will be the largest divisor you're looking for. Jul 23, 2025 · Find LCM of Two Numbers Using the GCD (Greatest Common Divisor) In this example, the function lcm_using_gcd(a, b) utilizes the property that the LCM of two numbers a and b is equal to their product divided by their greatest common divisor (GCD), calculated using math. Jul 14, 2025 · At least one of the two values in any such pair must lie within the range [1, √n]. If a number factors as n = p^a * q^b * * r^c then it will have (a+1)*(b+1)**(c+1) divisors. In Python 3, there are several approaches to efficiently calculate divisors of a given number. Find all divisors of a natural number | Set 1 In the above post, we found a way to find all the divisors in O (sqrt (n)). Apr 2, 2025 · In Python, finding common divisors can be achieved through various techniques, which we will explore in this blog. In this tutorial, we will walk through a simple yet effective Python program to find the common divisors of two Jul 11, 2025 · Given a number N, find the smallest prime divisor of N. Iterate from i = 3 to sqrt (N) and making a jump of 2. May 30, 2023 · In this article, we will understand two different methods to find the greatest common divisor (GCD) of two numbers in Python. In other words, the proper divisors of a number are the positive integers that divide the number evenly, leaving no remainder, but are less than the number itself. The individual counts are then summed up to get the final result. Oct 11, 2022 · A number is called a perfect number if the sum of its positive divisors excluding the number is equal to the number itself. GCD is the largest common divisor that divides the numbers without a remainder. Hello everyone. The divisor may be too large or too small resulting in ineffective learning. Find the smallest number with 2**500500 divisors. It is checked to see if the number divided by the iterator is 0. Prime factors are the prime numbers that divide a given number exactly without leaving a remainder. In this tutorial, we will learn how to write a Python program to check if a number is a perfect number. Cancel anytime. Let's explore different methods to find largest prime factor of a number in Python. Lets find divisors of 16. I'm doing this greatly in Javascript, C#, Java, but my Python code work only with print statement correctly. Mar 27, 2025 · This article contains Python programs that efficiently finds all the divisors of any given integer using different technique such as loop, math module, list comprehensions and set operations for concise and elegant solutions. In the end, this list is sorted. If the remainder is zero after the division, then it is divisible. 8. Oct 31, 2024 · One such mathematical problem is finding the common divisors of two numbers. Aug 11, 2025 · Write a Python program that determines if a given number is abundant by comparing the sum of its proper divisors to the number itself. In the way that I am going about this, the script is going to take a number from a range, determine the factors, determine if the Nov 15, 2020 · You know that there is a much faster way to find the number of divisors of a number than enumerating all the integers between 1 and n. Introduction In this tutorial, we will learn how to write a Python program to find all the divisors of an integer. So you need to check if the 16 / 4 == 4 (or in code N / divisor == divisor). A number is called an abundant number or excessive number if the sum of all of its proper divisors is greater than the number itself. Finding the sum of all the divisors of a number, without including that particular number that is being divided. You can write a code in Python that will help you find all the prime numbers. This guide will explain how to calculate the list of divisors using a simple algorithm along with a Python code example. Then the extracted element id is checked for divisibility with the divisor by using the modulo operator. 1s and the second one takes 1. Mar 31, 2025 · Learn different ways to find perfect numbers in Python, with explanations and code examples. Website: https://thecrazyprogrammer. Dec 5, 2023 · This post will show you three different ways to find the largest divisor of a number in Python. 9, python got built-in support for calculating gcd over a list of numbers. So the desired output is 4. If there is only one distinct prime divisor n = p 1 e 1 <math xmlns="http://www. Instead of lista, you can use list_divisors as the variable name as it is more readable. Then it loops through all the numbers from 2 to (num-1) and checks Jul 23, 2025 · The task of finding the GCD (Greatest Common Divisor) of two numbers in Python involves determining the largest number that divides both input values without leaving a remainder. To check a number is divisible by a given number by checking the remainder is zero. 0 might need a change Jun 2, 2013 · Greatest Common Divisor or Highest Common Factor of two numbers, say a and b is the largest positive integer that divides both a and b. Step 1. You can use the one mentioned here. Mar 6, 2024 · Output: True This function is_perfect_number iterates from 1 up to the number (exclusive) and checks if each integer is a divisor. Understanding how to work with common divisors in Python can be useful in a wide range of applications, from simplifying fractions to solving more complex number theory problems. For example, if a = 60 and b = 48, the GCD is 12, as 12 is the largest number that divides both 60 and 48 evenly. First, the program takes an integer input from the user and initializes a list with 1 as its first element, because 1 is always a divisor of any number. Nov 6, 2024 · Explore optimized methods to quickly find all divisors of a number using Python, along with practical examples. For each such divisor d, also add n / d as the paired divisor. I was hoping some of the people here who have more experience than me might take a look at my program and give some advice on how to improve it, any advice would be really appreciated! About my program: Currently I’m working on a code that implements decomposition of any given number into prime factors. The number of divisors of a number can be found directly from its prime factorization. Oct 12, 2021 · Learn how to find the better divisor of a number using Python with this comprehensive guide and example code. com Instantly Download or Run the code at https://codegive. Our program will ask the user to enter a no. Here is the second example of list in python in which we will make a program to find all the divisors of a given number. A divisor of a number is a positive integer that divides the number without leaving a remainder. append (i) return sum (divisors) # print the value/output by calling the function in print Apr 16, 2021 · The number taken from user is displayed on the console. The number itself can range very high, so it really need Jul 7, 2015 · 20 From Project Euler problem 500 The number of divisors of 120 is 16. For example, number 20 has 5 proper divisors: 1, 2, 4, 5, 10, and the divisor summation is: 1 + 2 + 4 + 5 + 10 = 22. Examples: Input : n = 25 Output : 3 Divisors are 1, 5 and 25. want to find the divisors of lots of numbers, generating all the primes up to root (n) with a sieve and then generating the prime decomposition, and iterating over it to get all the factors, will be much faster. Write a Python program to find all divisors of an integer or number using for loop. For example, all possible divisors of the number 36 are 1, 2, 3, 4, 6, 9, 12 and 18. A perfect number is a special number where the sum of its proper divisors (excluding itself) equals the number. Method 2: Using List Comprehension Python’s list comprehension feature can be used for a Nov 22, 2024 · A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding the number itself). If you enjoy solving number problems, checking for perfect numbers in Python is a great way to practice. In this Program, you’ll learn how to check Apr 4, 2022 · A simple python program to display all divisors of a number, which means printing all the numbers which are divisible by a given number in some range. Print the number of common factors of a and b. Number 'y' is called divisor of number 'x' if 'x/y' is 0. number: Input parameter representing the number for which the smallest divisor is to be found. For example: Input: 12 Output: 2 2 3 Let's explore different methods to find all prime factors of a number in Python. w3. One possible way to do this would be to fill the tower with blocks of size 1 Oct 29, 2025 · Given a number n, the task is to print all of its prime factors. D) of two numbers is the largest positive integer that perfectly divides the two given numbers. Each such power, k, contributes a factor of k+1 to the total number of divisors. Simple step-by-step guide with full code examples. Oct 11, 2025 · Given a positive integer N, the task is to write a Python program to check if the number is Prime or not in Python. Find DivisorsThis video is about finding divisors of a number and returning all of them in a list. Aug 24, 2023 · Sum of divisors We can use the same argument of the previous section. The task of finding all divisors of an integer is a common problem in programming and mathematics. Feb 12, 2022 · For example, let us take the number 12 and the divisors of 12 are 2, 3, 4, 6, and 12. This operation is essential for algorithms related to number theory, such as finding prime numbers or factoring composite numbers. May 24, 2025 · Python Exercises, Practice and Solution: Write a Python program to find the total number of even or odd divisors of a given integer. Jul 23, 2011 · Can someone explain to me an efficient way of finding all the factors of a number in Python (2. If any of the numbers divide N then it is the smallest prime divisor. In this post, we have explained a simple technique that will help you not only calculate the number of divisors of 1728 but you will look at the techniques to solve the various kinds of problems on the divisors of a number. If there is no numbers in the list it can be divided by, then it s May 30, 2025 · Python Programming Puzzles Exercises, Practice and Solution: Write a Python program to find the largest integer divisor of a number n that is less than n. Calculate the divisors of a positive integer online. Perfect for students learning DSA and preparing for competitive programming. Jun 29, 2016 · 2- In the amicable method you are looping 1 to n to find all the factors for both of the numbers. Aug 14, 2023 · Efficient approach is to observe the function and co-relate the pattern. If it is, it adds that number to sum_of_divisors. We will learn how to use a for loop or how to use the next() function to calculate the largest divisor with examples. I'm surprised you had the patience to find the number of factors 8388608. We'll delve into the logic behind finding divisors, summing them efficiently, and checking for perfect number properties. import math def smallest_divisor(p,n): #returns the smallest divisor of n which is greater than p for d in range(p+1,1+math. >1_000_000), then you need a much more clever algorithm. To find the GCD or HCF, we must pass at least one non-zero value. Input: n = 25 Output: [5, 5] Explanation: The prime factorization of 25 is 52. F) or greatest common divisor (G. sqrt(n))): if n % d == 0: return d return n def divisors(n): divs = 1 p = 1 while Jan 14, 2017 · A factor of a number x is a number y if y divides x without leaving a remainder. Oct 15, 2024 · Given a positive integer n, we have to find the total number of divisors for n. If it does, you will only add it once. Jul 23, 2025 · In other words, a divisor is an integer that, when multiplied by a whole number, results in the original number without any fractional or remainder part. For example, 6 is a perfect number because 1 + 2 + 3 = 6. After completion, it checks if the sum of these divisors equals to the original number to determine if it’s perfect. A perfect number is a number that is the sum of its proper divisors. Input : 100 Output : 9 Divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100 Approach 1: A Naïve Solution would be to iterate all the numbers from 1 to sqrt (n), checking if that number divides n and incrementing number of divisors. Naive Approach The naive approach to calculate divisors involves iterating through all numbers from 1 to the given Mar 2, 2024 · Problem Formulation: We often encounter a situation where we need to find common factors or divisors of two given integers. The highest common factor (H. To do that, we can use one of the three techniques below: Using the built-in gcd() function Using a while loop Using recursion to implement the Euclidian Algorithm Using the built-in gcd () function The easiest is to use the built-in Jul 23, 2025 · Write a Python program for a given number “n”, the task is to find its total number of divisors that are even or odd. However there is I developed the following Python functions when solving a few Project Euler problems, and since I'm not that familiar with Python, I'm curious at how I could improve them. For Example: Input: n = 6 Output: 3 Explanation: prime factors of 6 are 2 and 3, and the largest among them is 3. Highest Power of a Number in a Factorial Before you check this post, can you answer the number of divisors of 1728. In this Python example, the for loop iterate from 1 to a given number and check whether each number is perfectly divisible by number. We will show you how to go over the each number, find if i To print all the divisors of a given number, we will check whether each number starting from 1 to the given number divides the input number or not. For the number to find its divisors iterate from 2 to that number and check any one of them is a divisor of the given number. Apr 28, 2017 · Here is an approach that determines the multiplicities of the various distinct prime factors of n. For example if we want to find the divisors of number 6 they would be 1,2,3. Range will go from 2 to 5 = we check numbers 2 to 4. May 28, 2022 · Subscribed 0 118 views 2 years ago How to find divisors of a number in Python / Sympymore May 12, 2024 · The list of prime factors of a number is a list of prime numbers that multiply together to give the original number. The common divisors of two numbers are the divisors that both numbers share. How to Find Divisors of a Number? There are a few ways to find out divisors of a number: Brute Force Method: List out all the factors of the number, beginning with 1 and itself. Mar 3, 2024 · Method 1: Iterative Search This method involves searching for divisors by iterating from 1 to the square root of the number. For every prime factor pi, it can be included x times where 0 ? x ? ai. Example:. Know more and learn how to code in Python. org/1998/Math We would like to show you a description here but the site won’t allow us. Then it should return the index of the list that the number is able to be divided by. Note: Negative numbers (e. Write a Python function that takes an integer and returns the sum of its divisors, then test it with numbers 8 and 12. No cable box or long-term contract required. I'm guessing you are looking for the number of non-unique prime divisors because if you didn't want that I code just write a program to always return 1 if the number to factor is one and 2 if it's anything else. Jul 29, 2019 · Using unique prime factorisations and itertools to find all the divisors of a number. We used a concept of 'For Loop' and decision making (if-else). All prime numbers This program takes an integer input from the user and finds all the divisors of that number. Taking User Input number = int (input ("Enter an Jan 10, 2024 · Divisor calculation is a fundamental operation in mathematics and computer science. Examples: Input: n = 18 Output: [2, 3, 3] Explanation: The prime factorization of 18 is 2×32. For example, given a number 29, it has no divisors other than 1 and 29 itself. It's a different problem, if you think it's not then look for "Divisor function" on wikipedia. The better idea is to pad dataset with samples randomly selected from the whole dataset to make it divisible by optimal batch size. Dec 7, 2024 · def smallest_divisor (number): def: Declares a new function. Imagine that we have a tower of height 12 using equal size blocks, we need to find the size of all the blocks that can make the height exactly 12. in Python len([i for i in range(1,n+1) if n % i == 0]). Divisors are numbers that divide another number without leaving a remainder. If you want the implementation of the same using a Python program, you are in the right place. Mar 23, 2023 · The most optimized way to find the sum of divisors of a number for numbers in a given range in python Asked 2 years, 7 months ago Modified 8 months ago Viewed 876 times Jun 24, 2012 · The greatest common divisor (GCD) of a and b is the largest number that divides both of them with no remainder. Jan 8, 2022 · If you numbers are small, then precompute a list of prime divisors. finxter. Jan 17, 2023 · Hi! I’m a beginner at python, and currently self-teaching myself. Common divisors are numbers that divide both the numbers perfectly. For huge numbers, this problem is very hard to solve efficiently (this is an open math problem). For a given number n, every number from 1 to n contributes its presence up to the highest multiple less than n. 7)? I can create an algorithm to do this, but I think it is poorly coded and takes too long to produc Jul 23, 2025 · The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), is the largest positive integer that divides two or more numbers without leaving a remainder. 0 I want to find all divisors of a number in Python. input > 10, 15 Output > 2 The common factors of 10, 15 are 1 and 5 My code In this tutorial, we will learn how to find if a number is an abundant/excessive number or not using python. Input : n = 24 Output : 8 Divisors are 1, 2, 3, 4, 6, 8 12 and 24. Oct 6, 2021 · Level up your programming skills with exercises across 52 languages, and insightful discussion with our dedicated team of welcoming mentors. For instance, Let n = 6, => F(1) + F(2) + F(3) + F(4) + F(5) + F(6) => 1 will occurs 6 times in F(1), F(2), F(3), F(4), F(5) and F(6) => 2 will occurs 3 times in F(2), F(4) and F(6) => 3 will occur 2 times in F Sep 21, 2008 · Given your reqs coming up with the number of factors is vague. Using For loop (Static Input) Using For loop (User Input) Have you mastered basic programming topics of java and looking forward to mastering advanced topics in a java programming language? Master the concept of finding divisors of a number with efficient algorithms, detailed explanations, and practical coding examples. This approach takes O (sqrt (n)) time. It will then find out the lowest divisor of the number. It uses a for loop to iterate from 2 (the smallest prime divisor possible) to the input number. May 13, 2016 · I'm interested in tips for my algorithm that I use to find out the divisors of a very large number, more specifically "n over k" or C (n, k). Jul 22, 2019 · 2 Looking for the largest divisor is not a good approach because of two reasons. One way to find the GCD of two numbers is Euclid’s algorithm, which is based on the observation that if r is the remainder when a is divided by b, then gcd(a, b) = gcd(b, r). Nov 11, 2021 · For example, 8 isn't a prime number, as you can divide it by 2 and 4 (we can't use divisors equal to 1 and 8, as the definition prohibits this). C. The size of array might be prime number. Examples: Input: 25 Output: 5 Input: 31 Output: 31 Approach: Check if the number is divisible by 2 or not. Oct 30, 2025 · Given a positive integer n (1 ≤ n ≤ 1015), the task is to find its largest prime factor the biggest prime number that divides n exactly. Note : Prime number is a natural number greater than 1 that has exactly two factors:1 and itself. Contribute to reedhop24/python-codewars-8kyu-7kyu development by creating an account on GitHub. Jul 23, 2025 · Given a natural number n, print all distinct divisors of it. Examples: Input : 18 Output : 6 Divisors of 18 are 1, 2, 3, 6, 9 and 18. Method 1: Brute Force Mar 2, 2024 · This function sum_of_divisors() iterates through all the numbers from 1 up to the given number n, checks if they are divisors of n, and if so, calculates the number of their divisors using the inner count_divisors() function. This is a common requirement in various mathematical computations and coding challenges. Edit: To further improve your algorithm you can iterate through odd numbers only (after checking if you number is even) or, even Jan 15, 2022 · I would like to know, how I can add up all possible divisors of a number in python without the given number itself. smallest_divisor: The name of the function, which finds the smallest divisor of a given number. 7. If yes, it is appended to the empty list. For example you can use the Fermat's factorization if the numbers are not too huge (eg. As a base case, we can use gcd(a, 0) = a. Feb 21, 2020 · How to get the sum of all the divisors of a number, without including it Asked 5 years, 9 months ago Modified 5 years, 1 month ago Viewed 5k times In this tutorial, you will learn that how to get the smallest prime divisor of a number for which you get the input from the user. This step-by-step tutorial helps you master basic logic and efficient divisor detection. How do you compute the sum of the divisors of an integer in Sage? Sage uses divisors(n) for the list of divisors of n, number_of_divisors(n) for the number of divisors of n and sigma(n,k) for the sum of the k -th powers of the divisors of n (so number_of_divisors(n) and sigma(n,0) are the same). Returning the List of Divisors return divisors return divisors: Returns the complete list of divisors after the loop finishes. Explanations and method of finding all divisors of a number with examples. In this article we will explore All Divisors of a Number in Python. Jul 23, 2025 · For Loop In this example, we will use Python for loop to iterate over each element in the list. The first item of tuple is a number that division method takes and tries to divide by the smallest divisor starting from second item and finishing with square root of this number. Jul 12, 2025 · Now all the possible divisors can be generated recursively if the count of occurrence of every prime factor of n is known. If none of them divide, then N is the answer. Such numbers have a unique balance, making them interesting to learn about. You need a better algorithm to find the factors. For example, 1000 is a divisor for 2000, but your approach would miss the case. Here’s how I wrote find the number of divisors of nLive TV from 100+ channels. Jul 17, 2022 · In this video, we discussed about how to find all possible divisors of a natural number using Python Programming. < 1G). Here the task is simpler, we need to count divisors. When it finds the first number that divides the input number without leaving a remainder, it returns that number as the smallest divisor. com title: finding divisors of a number in python: a step-by-step tutorial introduction: finding divisors of a number is a common task in May 13, 2025 · Learn how to find the smallest divisor of a number in Python. Read the questions and the answer before posting, if you do not understand what is the topic just don't add not useful and already given answers. append (i): Adds the number i to the divisors list if it is a divisor of number. How to find all the divisors of a number in Python | python find divisorsyour queriesPython program to print divisors of a number using fo Sep 26, 2021 · This tutorial is to show you how we can find out the smallest divisor of a number in python. Using euclidean algorithm Euclidean algorithm repeatedly replaces the larger number with the remainder Oct 3, 2025 · Given a number n, find all prime factors of n. Feb 21, 2020 · I need to write a function func that will make such output print (func (6)) # Should be print out 1+2+3=6 Feb 20, 2011 · So the function inputs a list, and a number. gcd() method returns the greatest common divisor of the two integers int1 and int2. For example, given the numbers 12 and 18, we want to know the total number of common divisors, which in this case are 1, 2, 3, and 6. If you have a list of primes, this is a simple way to get the factorization: Oct 1, 2018 · In my program, it is supposed to ask the user for a number, then displays all the divisors possible, but in the end, it has to display the sum of all the divisors. In this python program, we are finding the lowest divisor using mod operator, for loop and if condition. Write a Python program to find the GCD of two numbers using While Loop, Functions, and Recursion. py #python program to find sum of all divisors of a number #lets create a function which performs the entire operation along with a parameter def sum_div (number): divisors = [1] for i in range (2,number): if (number % i == 0): divisors. ceil(math. The Greatest Common Divisor is also known as the Highest Common Factor (HCF), Greatest Common Factor (GCF), Highest Common Divisor (HCD), or Greatest Common Measure (GCM). For example, 28 is a perfect number because the sum of its divisors, 1 + 2 + 4 + 7 + 14 is equal to 28. We have discussed different approaches for printing all divisors (here and here). Each divisor has to be a combination of the primes in the factorization. Let’s look at the methods below to check for a prime number: Using flag variable We can check if a In this post, we discuss formulas for getting the number of divisors of a number and their sum, additionally we will implement an algorithm that solves this problem. A proper divisor of a number is any divisor of that number other than the number itself. com title: finding divisors of a number in python: a step-by-step tutorial introduction: finding divisors of a number is a common task in Here you will learn how easily we can find all the possible divisors of an integer in Python. How to find Greatest Common Divisor in Python Now, let’s look at how we can use Python to find the greatest common divisor of two numbers. How to find the smallest divisor in python? May 24, 2025 · Python Exercises, Practice and Solution: Write a Python program to find common divisors between two numbers in a given pair. Dec 6, 2017 · You are iterating in the range of [1, 100) only for the divisors, however, to find all divisors with this naive approach, you would ideally need to iterate over range of [1, num). Jan 6, 2025 · Prime numbers are a subset of natural numbers whose factors are only 1 and the number itself. Write a Python function to list all abundant numbers in a given range and then print them. Dec 5, 2024 · A prime number is a natural number greater than 1 and it does not have any divisor other than 1 and itself. Examples: Input: n = 10 m = 3 Output: Quotient: 3 Remainder 1 Input n = 99 m = 5 Output: Quotient: 19 Remainder 4 Method 1: Naive approach The naive approach is to find the quotient using the double division (//) operator and remainder using the modulus (%) operator. Sep 14, 2012 · You can find all the divisors of a number by calculating the prime factorization. append (i) divisors. Here, we will learn what are common divisors, a method to find the common divisors and a Python program to find the common divisors of two numbers. It's simple enough to count the divisors of n, eg. divisor 2 (add 2 because of divisors 2 and 8) here comes the problem, you can only add divisor 4 ONCE 4*4 is 16, but you do not want to count duplicates. See full list on blog. Instantly Download or Run the code at https://codegive. Hence, it is a prime number. c I need a code to find the common prime factors of three numbers in Python 3 Whenever I run it shows me the wrong HCF / GCD. g. Mar 15, 2025 · Learn how to find the Greatest Common Divisor (GCD) in Python using the Euclidean Algorithm. Divisors are numbers that can divide the specified number without leaving any remainder. It will reduce your O(n) complexity to O(sqrt(n)) for finding factors. Any number can be the perfect number if the sum of its positive divisors excluding the number itself is equal to that number. What better way than to take an example to understand what the definition means. For example, 6 is a perfect number in Python because 6 is divisible by 1, 2, 3, and 6. Edit: clarifying that the factorization can have many terms. Examples: Input : n = 10 Output: Even Input: n = 100 Output: Odd Input: n = 125 Output: Even Python Program for Check if count of divisors is even or odd using Naive Approach: A naive approach would be to find all the divisors and then see if the total number of divisors is In this video, I will show you how to find all of the divisors of a number in a Python program using a for loop and then using recursion. Using factorint () sympy provides the function factorint We would like to show you a description here but the site won’t allow us. Using Sieve of Eratosthenes In this method, we precompute smallest prime factor for every number up to n using a The above code for perfect number in python defines a function is_perfect_number (num) that checks if a number is perfect by summing its proper divisors (excluding the number itself) and comparing the sum to the number. Aug 11, 2025 · Write a Python program to compute and print the sum of all proper divisors of a given number. Your problem is the reverse, but you now have all the steps to work backwards. The first element of the sorted list is displayed on the console, since this is the smallest divisor. For example if N is divisible by 3 then you'll need 2 iterations to find the answer - in your case it would be about N/6 iterations. Introduction In this lab, we will write a C++ program to find the divisors of a given number. If your numbers are big (eg. The task is to find the quotient and remainder of two numbers by dividing n by m. Finding the GCD of two numbers a and b Step 1: List all the divisors of the number 'a'. Mar 6, 2024 · Output: 3 This example shows a simple function find_smallest_divisor(), which receives an integer as its parameter. On the other hand, 7 is a prime number, as we can't find any legal divisors for it. Note: For a prime number like 13 17, the smallest divisor will be the number itself. This is a Python Program to generate all the divisors of an integer. -13) are not considered prime number. In fact 120 is the smallest number having 16 divisors. 1 5 Program to Find Common Divisors of Two Numbers in Python Below are the ways to find the common divisors of the given two numbers in Python. gcd(). This is O (n). Sep 6, 2025 · Learn how to write a Python program to check perfect numbers with loops, functions, and recursion. Examples: Input : n = 10 Output: 1 2 5 10 Input: n = 100 Output: 1 2 4 5 10 20 25 50 100 Input: n = 125 Output: 1 5 25 125 We strongly recommend referring to the below article as a prerequisite. It’s simple and guarantees to find one of the better divisors of the number because the search stops as soon as a divisor is found, avoiding unnecessarily large divisors. Nov 24, 2021 · In the previous article, we saw how we can determine a Prime Number using Python logic and syntax. If any number divides the input number without leaving any remainder, then it is considered a divisor of the given number. But I don't want to print divisors, I want to assign them to some variable, or displaying them calling function in print. It then returns the computed LCM. Mar 22, 2015 · 37 As of python 3. We would like to show you a description here but the site won’t allow us. It is available in the math module and returns the largest positive integer that divides both numbers without leaving a remainder. Below is the implementation of the above approach: The math. Table of Contents How to find GCD of two numbers? How to find GCD of a list of numbers? Python implementation to find GCD of a list of numbers: C++ implementation to find GCD of a Python Program to find Perfect Number How to write a Python program to find Perfect Number using For Loop, While Loop, and Functions. This article explores different techniques and provides examples to demonstrate their effectiveness. Jan 16, 2024 · @wim I'm doing a for i in range (2, 100000): find_divisors (j) and the same with find_divisors_v2 and the first one takes 2. 1s (rough average). Oct 5, 2008 · Calculating the number of divisor of a given number doesn't need to calculate all the divisors. Give your answer modulo 500500507. If it returns 0, then that number is added to another list that contains all the elements that were divisible by the divisor. Jul 12, 2025 · Better Approach: Iterate over the first N natural numbers using a loop variable. That is if x % y == 0 we say that y is a factor of x. I'm practicing the basics of Python and I had a exercise of doing a function that asks for the user for a number and the function will return him all the divisors of that number so I done this def Feb 11, 2025 · Learn how to write C++, C, Python & Java programs to find the divisors of a positive integer and print them all, excluding the number. Dec 13, 2023 · Given a number n, count all distinct divisors of it. Method 2: Sieve of Eratosthenes Concept Sep 10, 2020 · Hence, the GCD is 6. You can find the list of prime factors of a number using a simple Python function. . Dec 7, 2024 · 6. Oct 10, 2019 · A prime number is a natural number greater than 1 and it does not have any divisor other than 1 and itself. So, we can: Iterate from 1 to √n to find all divisors less than or equal to √n. e. Adding Divisors to the List python Copy code divisors. The code consists of a d Jul 23, 2025 · A proper divisor of a natural number is the divisor that is strictly less than the number. Take care not to duplicate the square root divisor if n is a perfect square. May 13, 2025 · Learn how to find the smallest divisor of a number in Python. If I increase the values, find_divisors_v2 does even better in comparison Jul 23, 2025 · Given two integer numbers, the task is to find the count of all common divisors of given numbers? Input : a = 12, b = 24 Output: 6 Explanation: all common divisors Finding the divisors of a given number is a common problem in programming and mathematics. Nov 5, 2014 · If this is a repeated algorithm, i. The number range is iterated over. I am trying to write a Python script that will find prime numbers. Then it adds all the divisors and returns the sum of all the divisors as output. Jun 14, 2025 · gcd () function in Python is used to compute the Greatest Common Divisor (GCD) of two integers. Write a Python script to calculate the sum of divisors for a range of numbers and output the number with the highest divisor sum. Table of Contents How to find the factors of a number? Brute Force Python Implementation to find factors of a number Efficient method to find factors of a number Efficient Python Implementation to find factors of a number Efficient C++ Implementation to find sum-of-divisors. The above code for perfect number in python defines a function is_perfect_number (num) that checks if a number is perfect by summing its proper divisors (excluding the number itself) and comparing the sum to the number. This article provides the methods on how to find the GCD (Greatest Common Divisor) and will discuss 3 different methods for it. Using recursion, loops, and built-in methods. For example, 6 has proper divisor 1,2 and 3. Get your result in only four lines of code. Jul 15, 2025 · Given two numbers n and m. texnuo oyzt xxtyht ypetd tavac jbfbj mjouz bvx ldd mvl oirov eapz aqdg vbyfo togxek