Maximum divisors in a range. Your program only has to print out one of them.

Maximum divisors in a range. By using threads, your program will take less time to do the computation when it is run on a multiprocessor computer. 8 has 4 divisors. If 2 or more integers are found, return the lowest integer among t Can you solve this real interview question? Insert Greatest Common Divisors in Linked List - Given the head of a linked list head, in which each node contains an integer value. This calculates the maximum number of divisors of any positive integer less than n, given n as input. Dec 8, 2022 · thanks for your code, but the practice wants me write the number with its own divisor counts, for example for the inputs I gave it in the question, the answer should be: 594 16 so it means 594 is the maximum value with maximum number of divisors. Related tasks Amicable pairs {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"Arithmetic Progression(Arrays)","path":"Arithmetic Progression(Arrays)","contentType":"file Two part question: Trying to determine the largest prime factor of 600851475143, I found this program online that seems to work. A number is a beautiful number if it satisf Jun 24, 2012 · The greatest common divisor (GCD) of a and b is the largest number that divides both of them with no remainder. Examples: Input: N = 4 Output: 2 Input: N = 8 Output: 3 Naive Approach: In this approach, the idea is to generate all the numbers having exactly N divisors and check for the maximum number of prime divisors. However, it doesn't matter since you only want to find the number with the largest number of divisors, and not that number of divisors. To do this, we can iterate through all possible values of a and b, where a^2 + b^2 ≤ 10^14. 718 = A001113. a (1) = 4 since 8 has 4 divisors and that is the record for 1-digit numbers. python python-3. Probability Distributions showing Semi-Range Limits and Divisors Jul 11, 2025 · The task is to print the number which has the maximum number of distinct prime factors of numbers in range M and N. Print the text Between L and H, P has a maximum of D divisors. The numbers are 2, 3, 5, and 7. Then at the end of the program, you May 22, 2024 · Given an interval [x, y], the task is to find the divisor that occurs maximum number of times except '1' in the divisors of numbers in the range [x, y], both inclusive. An example in Subsection 3. S : Usually in programming problems, the task will include several queries where each query represents a different number and hence precalculating the divisors for all numbers in a range at once would be beneficial as the lookup takes O (1) time in that case. We will learn how to use a for loop or how to use the next() function to calculate the largest divisor with examples. Codeforces. ,1000000]? If this is so, why are you checking all the possible divisors for each number in the range? whatever is the list of divisors for 10 is also in the list for 20, 30, . The source Max yields a definite result if all its arguments are real numbers. In some numerical work in [12] it appears that the even numbers in the range have density about 1 and the density of even numbers missing is 3 about 1 6. In the range [2,2] we have 2 which is the maximum divisor in range. Your program only In UVa 294, Divisors, we are asked to find the number with the maximum number of divisors in a given range. If d (n) denotes the number of divisors of a positive integer n, then a positive integer N is highly composite if d (N) > d (n) for all n < N. MAX should be a fixed constant declared at the top of your code no smaller than 20,000 and hopefully something like 100,000 or 200,000 (depending upon the speed of your computer). How can i find the total numbers whose % with z is 0 i. For example, the divisors of 12 are 1, 2, 3, 4, 6 and 12. A. use it to show the proper divisors of the numbers 1 to 10 inclusive. 6. A prime number is a positive The divisors are randomly generated from numbers between 1 and 20. 10 has 4 divisors. My Attempt. In case all divisors have equal occurrence, return 1. One of the examples from Section 3. Most Composite N is the list of Which integer between 1 and 10000 has the largest number of divisors, and how many divisors does it have? Write a program to find the answers and print out the results. Your program must create K Write a multithreaded solution for this Dec 9, 2020 · Problem description: You are given a segment [568023; 569230]. 5 has 2 divisors. Sep 21, 2008 · @sker: Is there a range of Values for which you need the divisors. Your program must create K Write a multithreaded solution for this Tool to list divisors of a number. For instance, if N were to be 11, the answer will be 18. The idea is to use nested loops to generate all possible combinations of x & y in range [l, r] and check if they are co-prime. Your program only has to print out one of them. You are given two integers a and b. Feb 24, 2023 · Finally, we obtain the number of divisors for all the numbers and store these in a segment tree that maintains the maximum numbers in the segments. In the range [3,7] we have 4 which is the maximum divisor in range. I put checks in in case the integer is less than 2. It then outputs information about such numbers, arranging them in ascending order. The format of (n+n), where n is an integer, is equivalent to the expression (n*2). Finally, we obtain the number of divisors for all the numbers and store these in a segment tree that maintains the maximum numbers in the segments. Jan 17, 2025 · Composite number: A number with more than two divisors. The problem is, I'm having a hard time figuring out how it works ex Dec 13, 2023 · Given a number n, count all distinct divisors of it. Here is the code in Java, Python, C, and C++ to find the biggest composite number with the most divisors in the range. docx from COMP 268 at Athabasca University, Athabasca. Feb 16, 2015 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Jun 8, 2022 · Approach: Create an array arr [] of the size (N + 1) where arr [i] stores the number of divisors of i. Now write a program that uses multiple threads to solve the same problem, but for the range 1 to 100000. (Here e is Euler's number 2. 9 has 3 divisors. If there exist multiple numbers, print the smallest one. check_divisor As mentioned in an answer to this question an integer less than n n with largest number of divisors can be found exploring the numbers x x of the form Jul 23, 2025 · Every number is a divisor of itself and 1. We provide a solution and guide you step-by-step on how Exercise 3. Feb 15, 2016 · It is perfectly returning 100 has 9 divisors 5 has 2 divisors 6 has 4 divisors. Revise the program so that it will print out all numbers that have the maximum number of divisors. The number with Aug 24, 2023 · The goal of this project is to translate the wonderful resource http://e-maxx. It is possible that several integers in this range have the same, maximum number of divisors. It represents the sum of the proper divisors of n, excluding n itself. Find the maximum element in this set S or report -1 if no Oct 5, 2008 · Calculating the number of divisor of a given number doesn't need to calculate all the divisors. Examples: Input : Q = 3 query1 = [2, 5] query2 = [2, 2] query3 = [24, 28] Output : 3 0 0 In first query, 2 and 5 are prime number in the range with maximum difference which is 3 Introduction This tutorial delves into the art of finding common divisors using Python, offering programmers and mathematicians advanced computational strategies to solve divisor-related challenges efficiently. Input: X = 1, Y = 10 Output: 3 6, 8, 10 are numbers with the maximum number of divisors. Sep 7, 2017 · Prove that the number $83160= 2 ^{3} \\cdot 3 ^{3}\\cdot 5 \\cdot 7 \\cdot 11 $ has the largest number of divisors among all integers $≤10^5$. Exercise 3. That is, out of all divisors 9 is maximum and so the number 100 should be printed. The number $83160$ is so-called highly So the question is in the title itself. The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which ⁠n m⁠ is again an integer (which is necessarily also a A better but still inefficient solution will not calculate the number of divisors of each x in that range, but check that x has n divisors: For example, if n = 2, and x is an even number, then there is no need to calculate the number of divisors: An even x has n = 2 divisors if and only if x = 2. Nov 5, 2023 · Complete code is written below :- ```python def divisible (max, divisor): count = 0 # Initialize an incremental variable for x in range (max + 1): # Complete the for loop if x % divisor == 0: count += 1 # Increment the appropriate variable return count print (divisible (100, 10)) # Should be 10 print (divisible (10, 3)) # Should be 4 print (divisible (144, 17)) # Should be 9 ``` Explanation Jun 22, 2022 · Which integer between 1 and 10000 has the largest number of divisors, and how many divisors does it have? Write a program to find the answers and print out the results. Mar 31, 2016 · a (1) = 1; for n > 1, a (n) = largest proper divisor of n (that is, for n>1, maximum divisor d of n in range 1 <= d < n). Dec 13, 2022 · Therefore, the maximum count of prime divisors of a number can have is the count of the prime factors (can be repetitive also) in the factorization of the count of factors of the number. Oct 28, 2016 · Given a range [a, b], a, b <= 2^31, we should find how many numbers in this range have a maximum number of unique divisors. My current one looks like this import math def divSum(num): result = 0 for i in Mar 16, 2023 · If (gcd (x,y)%i)=0, check if i lies in the range [a,b] and if it does store it in ans using max () function so that we get the greatest common divisor lying in the range. You'll also learn how to modify their standard behavior by providing a suitable key function. Nov 6, 2024 · Explore optimized methods to quickly find all divisors of a number using Python, along with practical examples. There are many ways of calculating the factors, and each method is better suited to a particular range. Jun 10, 2020 · In the range [2,10] we have 4 which is the maximum divisor in range. In the range , find the number, or numbers, that have the maximum number of divisors. It's a different problem, if you think it's not then look for "Divisor function" on wikipedia. Hooley's Delta function: maximum number of divisors of n in [u, eu] for all u. 4 has 3 divisors. 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. The property of this tree is that each of its nodes branches out to the nodes with a value equal to one of its divisors (exces maximum height the tree can have? Task Find the integer from a to b (included) with the greatest number of divisors. By exploring innovative techniques and optimization methods, readers will learn how to write more performant and elegant Python code for mathematical computations. Prime Factorization: Prime factorization is the process of breaking down a number into its prime factors. , 90, 100, . def divisible (max, divisor): ___ # Initialize an incremental variable for ___ # Complete the for loop if x % divisor == 0: ___ # Increment the appropriate variable return count print (divisible (100, 10)) # Should be 10 print (divisible (10, 3)) # Should be 4 print (divisible (144, 17)) # Should be 9 Question: MAX DIVISOR TREE - 1000 Let a tree exists with the root value N. To find the value of f (10^14), we need to count the number of proper squarefree Gaussian integers with a^2 + b^2 ≤ 10^14. ', where L, H, P, and D are the numbers as defined above. append (i) return divisors number = int (input ("Enter an integer: ")) divisors = check_divisor (number) print (f"The divisors of {number} are: {divisors}") Code Explanation 1. Count (Fibonacci) is the count of Fibonacci Numbers in that range. One way to find the GCD of two numbers is Euclid’s algorithm, which is based on the Mar 9, 2023 · Approach: The idea is to iterate from L to R and try to place the integer in a set such that the Greatest common divisor of the set remains 1. Examples: Input : 18 Output : 6 Divisors of 18 are 1, 2, 3, 6, 9 and 18. Now I need to get the number of maximum divisor. Examples >>> fromsympyimportsieve>>> sieve. C. Data Structure and Algorithms @Prep Oct 11, 2015 · If I understand correctly, you want all the divisors for each number in the range [1,. Naive Approach: The naive approach is to check all the numbers between a and b how many of them are n-divisor number for doing this find out the number of each divisors for each number . Plot of the number of divisors of integers from 1 to 1000. Find a number in the range 1 to 20,000 with the most proper divisors. It represents the sum of all the positive divisors of n, including 1 and n itself. A number in range that has 4 prime factors is 210 (2 x 3 x 5 x 7) Input : N = 3 Output : 1 Input : N = 5000 Output : 5 Method 1 (brute force): For each integer from 1 to N, find the We can loop over all prime numbers in range and try to reduce N to it's prime factorisation, which would help us count the number of factors of N. Use d (n) or $\tau (n). Formally, find the maximum value of gcd (a,b), where 1≤a<b≤n. 4. Counting number of divisors is a classic problem, and there exists a fast and simple way to do it. A list of (positive) divisors of a given integer n may be returned by the Wolfram Language function Divisors[n]. If there are no prime in the range then print 0. For each number, it prints its ordinal number, the number of divisors and the two largest divisors in descending order. That check will sometimes be hard, sometimes easy. There are two distinct prime numbers in the given range so the maximum difference can be found. For two integers x, y, the greatest common divisor of x and y is denoted . A divisor (or factor) of an integer number n is a number which divides n without remainder Jan 8, 2022 · Given a number n, I want to generate a sorted list of all the unique divisors of n (with no duplications). Depending on how you are checking the divisors of each number, it can be more efficient. 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. When a lookup is requested involving an odd number that has not been sieved, the sieve is automatically extended up to that number. If z is squarefree, we Demonstration, with Cuisenaire rods, of the first four highly composite numbers: 1, 2, 4, 6 A highly composite number is a positive integer that has more divisors than all smaller positive integers. Mar 26, 2020 · This program creates 4 threads, each finding the number of divisors for a specific range of numbers. Most Composite N is the list of Exercise 3. 4 discussed divisors. Sep 9, 2025 · Task Create a routine to generate all the proper divisors of a number. , 1000 etc. We respond to each query by querying the segment tree. For a range between numbers x and y. myprograms; import j Mar 24, 2017 · The second line finds the maximum number of divisors, and the third line marches through your divisors list and adds the corresponding number to the return list only if it has the maximum number of divisors. Now for every j from the range [1, N], increment all the elements which are divisible by j. What's reputation and how do I get it? Instead, you can save this post to reference later. 2: Which integer between 1 and 10000 has the largest number of divisors, and how many divisors does it have? Write a program to find the answers and print out the results. This can be done by storing the LCM of the set and each time before adding the element into the set check that the GCD of the number with LCM of the set remains 1. Implementation details limit the number of primes to 2^32-1. What about this do you not understand? Apr 23, 2021 · My teacher told me write this code only with one func it has to print the largest number of divisors between 20 numbers and if 2 number had same count of divisors print the largest one I writed t Exercise 12. Return the linked list after insertion. at the end of the program, output the elapsed time, the integer that has the largest number of divisors, and the number of divisors that it has. The greatest common divisor of two numbers is the largest Sep 14, 2025 · A divisor, also called a factor, of a number n is a number d which divides n (written d|n). The function should determine for all integers up to and including the maximum, if the number is evenly divisible by the divisor. . But is there an more efficient way? 793 asked Dec 04 '12 17:12 Nov 24, 2015 · In fact the number of divisors in the given range can be much larger than polylogarithmic, but I have not attempted to determine the maximum order of this quantity. Show all output here. 2 has 2 divisors. The task is to find the maximum difference between two prime numbers in the range for each query. $ Output For each range, find the number P which has the largest number of divisors (if several numbers tle for first place, select the lowest), and the number of positive divisors D of P (where P is included as a divisor). For Example: The standard uncertainty which is contributed to the combined uncertainty can be obtained by dividing the semi-range limits by a divisor. Use Sieve of Eratosthenes to mark the prime numbers and store the smallest prime divisor of each number. Order of integers in the array must be smalles HIS PAGE DISCUSSES ONE POSSIBLE SOLUTION to the following exercise from this on-line Java textbook. A ‘nice’ divisor is a factor that contributes to a product that assembles the original number through its multiplicative combination. Otherwise, use trial division by the known factors in the list to determine their multiplicities, and use those multiplicities to calculate the number of divisors. Count (Primes) is the count of Prime Numbers in that range. how many numbers between x and y are divisible by z ? For each value that is found in the array, one can look up the set of divisors, and compute the total number occurences of all the divisors. Please don't use $\sigma$ for the number of divisors (that should be the sum of the divisors). Problem Statement Given an interval [a, b]. Press the "Set the Difficulty" button to change the divisors. 3 has 2 divisors. e. Jun 10, 2020 · -1 Explanation: For 8 and 12, common divisors are [1,2,4]. Then 6 is the number that has the maximum number of divisors. Jan 18, 2025 · In this tutorial, you'll learn how to use Python's built-in min() and max() functions to find the smallest and largest values. Sums and products are commonly taken over only some Jul 29, 2019 · Here’s a problem I was trying to solve recently: given an integer n, what are all the divisors of n? A divisor, also known as a factor, is an integer m which evenly divides n. So the answer for above query is 4, as it is the maximum number of divisors a number has in [1, 10]. s (N) is the Restricted Divisor Function. After that, you will be given q queries each of which contains two integers low and high. The best algorithm I can imagine is an improved Sieve of Eratosthenes, with an array counting how many prime factors a number has. Print the text ‘Between L and H, P has a maximum of D divisors. x asked Feb 15, 2016 at 10:50 cloudybunny 129117 2 Answers Sorted by: 1 Jul 17, 2017 · Problem: For the integers in the given range find the number that has the most divisors. Jul 23, 2025 · Explanation: Only one pair {4, 5} is possible in the given range, so the maximum difference is 1. Find the divisor that appears the maximum number of times in a range of integers using a C++ function. Example: -Divisors of 5 are: 1-5. Show the number and just the count of how many proper divisors it has. Use an array as follows: As you count the divisors for each number, store each count in an array. This expression ensures the resulting integer will be an even number. I ended up writing something with itertools, and the code uses a couple of neat bits of number theory. Specifically, the problem aims to split the number into several factors that, when May 1, 2024 · The range of “n” will start at 0 and end at 9 (the end range value of 10 is excluded), with “n” incrementing by the default of 1 in each iteration of the loop. GeeksforGeeks | A computer science portal for geeks The code needs to initialize a variable to count the number of divisible values, iterate through the range of numbers from 0 to max - 1, and increment the count if the current number is divisible by divisor. Jul 25, 2023 · Learn how to find the max occurring divisor in a given interval with step-by-step explanations and examples. If there are multiple numbers with the same number of divisors, you'll get a list of them: Oct 15, 2022 · In C++, include cmath instead. ru/algo which provides descriptions of many algorithms and data structures especially Jul 25, 2023 · Learn how to find the max occurring divisor in a given interval with step-by-step explanations and examples. 6 has 4 divisors. Dec 7, 2024 · def check_divisor (number): number = abs (number) divisors = [] for i in range (1, number + 1): if number % i == 0: divisors. For each number from 1 to 100 you can check all of it's multiples and add the number of divisors. GAME: Rax will randomly provide you a range [ L , R ] (both inclusive) and you have to tell him the maximum difference between the prime numbers in the given range. You can change the range of divisors between a minimum of 1 and a maximum of 31. The Integers 1 to 10000 Range is a range of numbers, in groups of 100. All ranges are below 100005. With our GCD calculator you will find the greatest common divisor of a set of numbers in the blink of an eye. To know how to calculate divisors using prime factorisation, click here. Let’s define S as the set of common divisors of a and b which lie in the range low to high i. your task is to determine sum of all beautiful numbers in the range land r. At the end of the program, output the elapsed time Nov 15, 2020 · This code will collect the maximum number of divisors in a list, resetting the list if a greater number is found, and appending to the list otherwise. Programming competitions and contests, programming communityLet's consider all integers in the range from 1 1 to n n (inclusive). The greatest common divisor This function takes a numerical interval as input and finds the numbers within the range that have the maximum number of different divisors. Function Definition def check_divisor (number): def: Declares a new function. Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Then at the end of the program, you Jul 23, 2025 · Output : 4 There are four numbers with 2 divisors in range [1, 7]. In the SVG file, hover over a bar to see its statistics. Find the maximum sum of factors of numbers from 1 to N. Between every pair of adjacent nodes, insert a new node with a value equal to the greatest common divisor of them. Mar 31, 2021 · He wants to play the game with you. ’, where L, H, P , and D are the numbers as defined above. The source code for Feb 7, 2012 · Given the range [1, 2 Million], for each number in this range I need to generate and store the number of the divisors of each integer in an array. [1][2] In the name "greatest common divisor It seems likely that the asymptotic density of even numbers in the range of s exists. Mar 18, 2022 · The basic idea is splitting the prime powers into four sets with roughly the same number of divisors each, listing the divisors, and generating divisors from two pairs of two sets dynamically using min-heaps, and combining as expected. In the range [5,6], there lies no divisor so we print -1. Thank you. 2 asked you to find the number in the range 1 to 10000 that has the largest number of divisors. Click on the range for more information about that range. Write a function that takes two inputs: a Divisors [n] gives a list of the integers that divide n. In [1] it is shown that the lower density of the set of even numbers missing from the range is at least 0:06. The function uses the divisor function from the math Dec 16, 2023 · since you need a count of values for which value%divisor == 0 and it should be between [0, max), where max is not inclusive then what you can do is just (max_value-1)//divisor + 1 number of value for which a number is divisible by divisor with no remainder, +1 is for value 0 so your solution should be def divisible(max_value, divisor): Feb 17, 2020 · I made this so I can feed it integers and return an array with all the divisors of that integer. Print the result as the output. Solution: package com. Fortunately, we can tweak the Eratosthenes sieve to count the number of divisors more efficiently and elegantly. For each pair (a, b) that satisfies the condition, we check if the Gaussian integer z = a + bi is squarefree by checking its prime factorization. Now largest divisor for any number will be number / smallest_prime_divisor. Also, it's not the square root that you want to multiply by two, it's the number divisors. Then you just count those in the range with a number of divisors equal to x. Plus it would break for perfect squares, though I don't think a perfect square can be the answer unless the range is tiny. There are three answers possible for the given range. If it is equal to n then it is a n-divisor number Efficient A list of prime numbers, implemented as a dynamically growing sieve of Eratosthenes. In this guide, we explore a programming issue where a script fails to identify all numbers with the maximum divisors within a given range. The greatest common divisor of two numbers is the largest positive integer that evenly divides both numbers. low <= d <= high. Output For each range, find the number P which has the largest number of divisors (if several numbers tie for first place, select the lowest), and the number of positive divisors D of P (where P is included as a divisor). For integers, only positive divisors are usually considered, though obviously the negative of any positive divisor is itself a divisor. Apr 12, 2014 · In this problem all numbers are integers. For a Prime Number, Count (d (N))=2. -Divisors of 6 are: 1-2-3-6. ) Mar 21, 2023 · Here's the completed code for the "divisible" function: def divisible (max, divisor): count = 0 # Initialize an incremental variable for x in range (max+1): # Complete the for loop if x % divisor == 0: count += 1 # Increment the appropriate variable return count print (divisible (100, 10)) # Should be 10 print (divisible (10, 3)) # Should be 3 print (divisible (144, 17)) # Should be 9 In this Jul 12, 2025 · Given an integer N which denotes the number of divisors of any number, the task is to find the maximum prime divisors that are possible in number having N divisors. 7 has 2 divisors. Below are the steps Write a function that takes two inputs: a maximum and a divisor. You only had to print out one such number. For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. /* * This program counts the number of divisors for integers in the range * 1 to 10000. Max (Count (d (N))) is the highest number of divisors that any single number within that range possesses. The minimum number of divisors are $2$ (for primes), but the maximum number of divisors are what we are interested in. The source code for Jul 31, 2024 · Examples: L = 1 R = 10: 1 has 1 divisor. It is possible that several integers in this range have the same, maximum number Mar 22, 2021 · I've been asked this question somewhere . The result is then simply the array length, minus this total number of occurances of divisors. It cannot be more than the number itse In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. You are asked to find the integer in the range 1 to MAX that has the largest number of divisors. We iterate through the given range, find the divisors for each number, and track the number with the maximum divisors, ensuring that it's a composite number. ”, where L, U, P, and D are the numbers as defined above. n <= 10^18. 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. How I can do this? Any suggestions please. Find Exercise 3. Efficiently finding all the divisors of a number is an important algorithmic problem. Mar 23, 2023 · I would like to find the sum of divisors of a number for numbers in a given range in the fastest possible way. For Honors Credit, rewrite this function using a whileloop 2. 6: Exercise 3. The task is to find the number of elements in the range [X,Y] both inclusive, that have the maximum number of divisors. Dec 19, 2012 · If the list is empty, the number is prime, and the number a + i has two divisors. σ (N) is the Divisor Function. Can you solve this real interview question? Find Greatest Common Divisor of Array - Given an integer array nums, return the greatest common divisor of the smallest number and largest number in nums. The source code for that example Dec 13, 2016 · This is a question I've been doing on some online judge platform. Mar 18, 2023 · Write a program that uses multiple threads to solve the problem of finding the integer in the range 1 to 10000 that has the largest number of divisors, but for the range 1 to 100000. Formally, find the maximum value of gcd(a, b) g c d (a, b), where 1 ≤ a <b ≤ n 1 ≤ a <b ≤ n. Your program must create K threads Jun 1, 2021 · Given n queries of the form range [L, R]. Mar 3, 2024 · 💡 Problem Formulation: In this article, we tackle the challenge of finding the approach to maximize the number of ‘nice’ divisors for a given positive integer. See original problem Jul 11, 2025 · Given two numbers X and Y. Jun 23, 2022 · Given a number N, find the maximum number of unique prime factors any number can have in range [1, N]. you are given 2 integers l and r . Prime numbers only have two divisors - 1 and the number itself. Highly composite numbers are labelled in bold and superior highly composite numbers are starred. 2: Exercise 3. Find integer within given range that has the most natural dividers. _reset()# this line for doctest only>>> 25insieveFalse>>> sieve. Dec 5, 2023 · This post will show you three different ways to find the largest divisor of a number in Python. And you will see that this technique works not only for number of divisors, but also for generating sum of divisors, totient function, biggest prime divisor, basically all functions that have to do with divisors! Divisor Sieve O (n The Integers 1 to 10000 Range is a range of numbers, in groups of 100. Tags: c algorithm numbers How to find the smallest number in the the range 1 to 100 that has the most divisors? I know a trivial way would be to check the divisors of each number from 1 upto 100 and keep track of the number having maximum divisor. Return the string "Error" if a > b. Jul 23, 2025 · Use the max_prime_factors_prime_factorization (n) function to find the number between 1 and n that has the maximum number of distinct prime factors. May 9, 2021 · What is the best (or close) way to calculate the number of divisors of N which are in the closed integer interval [X, Y]? As of now, the best method I know is to get all primes till $\\sqrt N$, get In this video, we will discuss the solution to the problem Maximum divisors in a Range (MAXDIV) of the prepbytes platform. Finally, you'll code a few practical examples of using min() and max(). This function must use a for-loop B. Mar 27, 2024 · This article will discuss the problem of finding the maximum divisors in a range. So if x=p1^(a1)*p2^a2*p3^a3, where p1, p2, p3 are Question: Write a multithreaded solution for this problem. This approach takes O (sqrt (n)) time. Examples: Input: X = 2, Y = 9 Output: 2 6, 8 are numbers with the maximum number of divisors. In the range [2,10] we have 4 which is the maximum divisor in range. 2 discussed divisors. Jun 16, 2022 · View Excercise 3. The number of divisors is 4. For example: divNum(15, 30) ==> 24 divNum(1, 2) ==> 2 divNum(0, 0) ==> 0 divNum(52, 156) ==> 120 If there are several numbers that have the same (maximum) number of divisors, the smallest among them should be returned. Smaller numbers tend to have more divisors than larger numbers. For example, 6 is highly composite because d (6) = 4 . Print the text “Between L and U, P has a maximum of D divisors. Finally, it joins all threads and finds the overall integer with the largest number of divisors across all threads. It finds the maximum divisor count. Solving this problem is really straight forward, but what I'm interested in is the efficie May 5, 2013 · I have three numbers x, y , z. I'm having trouble with the last Count (d (N)) is the number of positive divisors of n, including 1 and n itself. Method 1: Traverse all the elements from X to Y one by one. 2 asked you to find the integer in the range 1 to 10000 that has the largest number of divisors. Nov 5, 2014 · P. Return ans once we are done with all the iteration in for loop One of the most easiest approach which I have thought is to first calculate total number of divisors of 'n' using prime factorization (by Sieve of Eratosthenes) of n and then subtract from it the Number of divisors of the number 'n' that are also divisible by 'k'. _listarray Jul 12, 2025 · Efficient approach: A better solution is to precompute the maximum divisor of the numbers from 2 to 10 5 and then just run a loop for array and print precomputed answer. The number of divisors is 2. Also check if gcd/i lies in the range and if it does then again update the value of ans using max () function. For each range, find the number P which has the largest number of divisors (if several numbers tie for first place, select the lowest), and the number of positive divisors D of P (where P is included as a divisor). Examples: Input : N = 500 Output : 4 The maximum number of prime factors for any number in [1, 500] is 4. Find the maximum occurring divisor in the range including both a and b, except 1 . Each thread updates a shared results list with the integer having the maximum divisors it found. Finally, find the largest such set of the integers. Upvoting indicates when questions and answers are useful. ohkrw htmok zsdc brwiwbp fxdlpium dkkbqg lbik tptei rnfovgk gvxggm