GCD (Greatest Common Divisor) Practice Problems for Competitive Programming Last Updated : 22 Mar, 2025 Comments Improve Suggest changes Like Article Like Report GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest positive integer that divides both of the numbers.GCD of Two NumbersFastest Way to Compute GCDThe fastest way to find the Greatest Common Divisor (GCD) of two numbers is by using the Euclidean algorithm. The Euclidean algorithm is an efficient and widely used method for GCD calculation. It used to compute GCD of two numbers in O(log(min(a,b)).It uses recursion to repeatedly replace a with b and b with the remainder of a divided by b until b becomes zero, returning a as the GCD. This approach is concise and efficient for GCD calculation.Below is the code snippet for above algorithm: C++ int gcd (int a, int b) { if (b == 0) return a; else return gcd (b, a % b); } Java public static int gcd(int a, int b) { if (b == 0) return a; else return gcd(b, a % b); } Python def gcd(a, b): if b == 0: return a else: return gcd(b, a % b) C# using System; int Gcd(int a, int b) { if (b == 0) return a; else return Gcd(b, a % b); } JavaScript function gcd(a, b) { if (b === 0) { return a; } else { return gcd(b, a % b); } } Identifying Problems that involve GCD (Greatest Common Divisor)GCD (Greatest Common Divisor) problems can vary in complexity and application, but they generally involve finding the greatest common divisor of one or more integers or applying GCD properties to solve a specific problem. Here are some common types of problems that involve GCD:Problems that require to determine if one number is divisible by another may involve GCD, as GCD is related to the greatest common factor of two numbers.Many number theory problems which related to coprime numbers, relatively prime numbers, or Euler's totient function, involve GCD calculation.Consider whether the problem hints about the need to factorize numbers into their prime factors. GCD problems sometimes involve prime factorization to find common factors efficiently.In graph theory, GCD can be used in problems related to connected components, in which a edge between the nodes will only exist if they are not co-prime.Here is a list of the Top GCD Problems for practice. Problems in this Article are divided into three Levels to practice according to the difficulty level step by step.Easy Level Problems on GCDProgram to Find GCD or HCF of Two NumbersCheck if two numbers are co-prime or notGCD of more than two (or array) numbersProgram to find LCM of two numbersLCM of given array elementsFind the other number when LCM and HCF givenMinimum insertions to make a Co-prime arrayFind the minimum possible health of the winning playerMinimum squares to evenly cut a rectangleMinimum operations to make GCD of array a multiple of kMedium Level Problems on GCDLCM of First n Natural NumbersGiven GCD G and LCM L, find number of possible pairs (a, b)Count numbers in range 1 to N which are divisible by X but not by YMinimum possible final health of the last monster in a gameFind the maximum GCD of the siblings of a Binary TreeCheck if possible to move from given coordinate to desired coordinateProgram to find Greatest Common Divisor (GCD) of N stringsLargest subsequence having GCD greater than 1Subsequence of size k with maximum possible GCDMinimum gcd operations to make all array elements oneGCD of elements in a given rangeCount pairs of natural numbers with GCD equal to given numberMaximum GCD of all subarrays of length at least 2Queries for GCD of all numbers of an array except elements in a given rangeMinimum operations required to make two numbers equalGCD of two numbers formed by n repeating x and y timesHard Level Problems on GCDRemove an element to maximize the GCD of the given arrayCommon divisors of N numbersFind the number of pairs such that their gcd is equals to 1Program to find Nth term divisible by a or bLargest number that divides x and is co-prime with ySummation of GCD of all the pairs up to NCalculate the Sum of GCD over all subarraysSum of LCM(1, n), LCM(2, n), LCM(3, n), … , LCM(n, n)Count number of pairs (A <= N, B <= N) such that gcd (A , B) is BFind original numbers from gcd() every pairCount number of sub-sequences with GCD 1Split array into minimum number of subarrays having GCD of its first and last element exceeding 1 Comment More infoAdvertise with us Next Article Program to Find GCD or HCF of Two Numbers M mridul_gfg Follow Improve Article Tags : Mathematical DSA GCD-LCM Practice Tags : Mathematical Similar Reads GCD (Greatest Common Divisor) Practice Problems for Competitive Programming GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest positive integer that divides both of the numbers.GCD of Two NumbersFastest Way to Compute GCDThe fastest way to find the Greatest Common Divisor (GCD) of two numbers is by using the Euclidean algorithm. The E 4 min read Program to Find GCD or HCF of Two Numbers Given two positive integers a and b, the task is to find the GCD of the two numbers.Note: The GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest number that divides both of them. Examples:Input: a = 20, b = 28Output: 4Explanation: The factors of 20 are 1, 2, 4 12 min read Check if two numbers are co-prime or not Two numbers A and B are said to be Co-Prime or mutually prime if the Greatest Common Divisor of them is 1. You have been given two numbers A and B, find if they are Co-prime or not.Examples : Input : 2 3Output : Co-PrimeInput : 4 8Output : Not Co-PrimeThe idea is simple, we find GCD of two numbers a 5 min read GCD of more than two (or array) numbers Given an array arr[] of non-negative numbers, the task is to find GCD of all the array elements. In a previous post we find GCD of two number.Examples:Input: arr[] = [1, 2, 3]Output: 1Input: arr[] = [2, 4, 6, 8]Output: 2Using Recursive GCDThe GCD of three or more numbers equals the product of the pr 11 min read Program to find LCM of two numbers Given two positive integers a and b. Find the Least Common Multiple (LCM) of a and b.LCM of two numbers is the smallest number which can be divided by both numbers. Input : a = 10, b = 5Output : 10Explanation : 10 is the smallest number divisible by both 10 and 5Input : a = 5, b = 11Output : 55Expla 5 min read LCM of given array elements In this article, we will learn how to find the LCM of given array elements.Given an array of n numbers, find the LCM of it. Example:Input : {1, 2, 8, 3}Output : 24LCM of 1, 2, 8 and 3 is 24Input : {2, 7, 3, 9, 4}Output : 252Table of Content[Naive Approach] Iterative LCM Calculation - O(n * log(min(a 14 min read Find the other number when LCM and HCF given Given a number A and L.C.M and H.C.F. The task is to determine the other number B. Examples: Input: A = 10, Lcm = 10, Hcf = 50. Output: B = 50 Input: A = 5, Lcm = 25, Hcf = 4. Output: B = 20 Formula: A * B = LCM * HCF B = (LCM * HCF)/AExample : A = 15, B = 12 HCF = 3, LCM = 60 We can see that 3 * 60 4 min read Minimum insertions to make a Co-prime array Given an array of N elements, find the minimum number of insertions to convert the given array into a co-prime array. Print the resultant array also.Co-prime Array : An array in which every pair of adjacent elements are co-primes. i.e, gcd(a, b) = 1 . Examples : Input : A[] = {2, 7, 28}Output : 1Exp 6 min read Find the minimum possible health of the winning player Given an array health[] where health[i] is the health of the ith player in a game, any player can attack any other player in the game. The health of the player being attacked will be reduced by the amount of health the attacking player has. The task is to find the minimum possible health of the winn 4 min read Minimum squares to evenly cut a rectangle Given a rectangular sheet of length l and width w. we need to divide this sheet into square sheets such that the number of square sheets should be as minimum as possible.Examples: Input :l= 4 w=6 Output :6 We can form squares with side of 1 unit, But the number of squares will be 24, this is not min 4 min read Like