# Find the GCD (Greatest Common Divisor) of two numbers using EUCLID'S ALGORITHM

Here, we are going to learn how to **find the GCD (Greatest Common Divisor) of two numbers using Euclid's Algorithm (C++ program)**?

Submitted by Ankit Sood, on November 11, 2018

**What is GCD?**

It is called as a **greatest common factor** or generally called as a highest common factor (HCF). For example, if we take two numbers **4** and **6** then the factors of these numbers are **1,2,2** and **1,2,3** so the common factors are **2** and **1** and **multiplication of these common factors is what we call as gcd** of these two numbers which in the above case is **2 X 1 =2** so **GCD (4,6) = 2**.

**Basic Euclidean Algorithm for GCD:**

The above algorithm stands on two basic facts which are stated below:

- If we try to decrease the bigger number by subtracting that number by the small then the gcd remains unaffected.
- The base case in our algorithm is when we divide the smaller number and remainder comes out to be zero then our algo stops.

**Description:** So basically avoid all the brute force approaches we can perform the required task in **O(log(min(a,b))** time using **Euclid's algorithm** which is an optimized approach as compared to the other approaches.

## C++ program to find GCD of two numbers using EUCLID'S ALGORITHM

#include<iostream> using namespace std; int euclidalgo(int x,int y) { if(x==0) return y; return euclidalgo(y%x,x); } int main() { int a,b; cout<<"Enter two numbers whose GCD is to be calculated: "; cin>>a>>b; cout<<"GCD of these numbers is: "<<euclidalgo(a,b)<<endl; return 0; }

**Output**

Enter two numbers whose GCD is to be calculated: 4 6 GCD of these numbers is: 2

Related Tutorials

- Introduction to Algorithms
- Introduction to Greedy Strategy in Algorithms
- Stability in sorting
- External Merge Sorting Algorithm
- Radix Sort and its Algorithm
- Bucket Sort Algorithm
- Bubble sort Algorithm, Flow Chart and C++ Code
- Insertion sort Algorithm, flowchart and C, C++ Code
- Merge Sort | One of the best sorting algorithms used for large inputs
- Binary Search in C, C++
- Randomized Binary Search
- Meta Binary Search | One-sided Binary Search
- Difference between Linear Search and Binary Search
- Binary Search in String
- Variants of Binary Search
- Sieve of Eratosthenes to find prime numbers
- Optimal Merge Pattern (Algorithm and Example)
- Given an array of n numbers, Check whether there is any duplicate or not
- Finding the missing number
- Find the number occurring an odd number of times
- Find the pair whose sum is closest to zero in minimum time complexity
- Find three elements in an array such that their sum is equal to given element K
- Bitonic Search Algorithm
- Check whether a number is Fibonacci or not
- Segregate even and odd numbers in minimum time complexity
- Find trailing zeros in factorial of a number
- Find Nearest Greatest Neighbours of each element in an array
- Interpolation search algorithm
- Floor and ceil of an element in an array using C++
- Two Elements whose sum is closest to zero
- Find a pair with a given difference
- Count number of occurrences (or frequency) in a sorted array
- Find a Fixed Point (Value equal to index) in a given array
- Find the maximum element in an array which is first increasing and then decreasing
- Dynamic Programming (Components, Applications and Elements)
- Algorithm for fractional knapsack problem
- Algorithm and procedure to solve a longest common subsequence problem
- Find the Nth Fibonacci number | C++
- Longest Common Subsequence using Dynamic programming (DP)
- Longest Increasing Subsequence using Dynamic programming (DP)
- Find the maximum sub-array sum using KADANE'S ALGORITHM
- Non-intersecting chords using Dynamic Programming (DP)
- Edit Distance using Dynamic Programming (DP)
- Finding Ugly Number using Dynamic Programming (DP)
- Egg dropping problem using Dynamic Programming (DP)
- Wild card matching problem using Dynamic programming (DP)
- Compute sum of digits in all numbers from 1 to N for a given N
- Minimum jumps required using Dynamic programming (DP)
- Graph coloring problem's solution using backtracking algorithm
- Breadth First Search (BFS) and Depth First Search (DFS) Algorithms
- Travelling Salesman Problem
- Kruskal's (P) and Prim's (K) Algorithms
- Multistage graph problem with forward approach and backward approach algorithms
- Floyd Warshall algorithm with its Pseudo Code

- Backtracking (Types and Algorithms)
- 4 Queen's problem and solution using backtracking algorithm
- N Queen's problem and solution using backtracking algorithm
- Compute the value of A raise to the power B using Fast Exponentiation
- Implement First Come First Served (FCFS) CPU Scheduling Algorithm using C program
- Implementations of FCFS scheduling algorithm using C++
- Implementation of Shortest Job First (SJF) Non-Preemptive CPU scheduling algorithm using C++
- Implementation of Shortest Job First (SJF) Preemptive CPU scheduling algorithm using C++
- Implementation of Priority scheduling (Pre-emptive) algorithm using C++
- Implementation of Priority scheduling (Non Pre-emptive) algorithm using C++
- Implementation of Round Robin CPU Scheduling algorithm using C++
- Analysis of LRU page replacement algorithm and Belady's anomaly
- Branch and Bound
- Find the roots of a complex polynomial equation using Regula Falsi Method in C
- Sieve of Eratosthenes to find prime numbers
- Implementations of FCFS scheduling algorithm using C++
- Implementation of Shortest Job First (SJF) Non-Preemptive CPU scheduling algorithm using C++
- Implementation of Shortest Job First (SJF) Preemptive CPU scheduling algorithm using C++
- Implementation of Priority scheduling (Pre-emptive) algorithm using C++
- Divide and Conquer Paradigm (What it is, Its Applications, Pros and Cons)
- Implementation of Priority scheduling (Non Pre-emptive) algorithm using C++
- Implementation of Round Robin CPU Scheduling algorithm using C++
- Jump Search Implementation using C++
- Optimal Merge Pattern (Algorithm and Example)
- Introduction to Greedy Strategy in Algorithms
- Strassen's Matrix Multiplication in algorithms
- Huffman Coding (Algorithm, Example and Time complexity)
- Backtracking (Types and Algorithms)
- 4 Queen's problem and solution using backtracking algorithm
- N Queen's problem and solution using backtracking algorithm
- Graph coloring problem's solution using backtracking algorithm
- Tournament Tree and their properties
- Deterministic and Non Deterministic Algorithms
- Lower Bound Theory
- Non Recursive Tree Traversal Algorithm
- Line Drawing Algorithm
- Breadth First Search (BFS) and Depth First Search (DFS) Algorithms
- P and NP problems and solutions | Algorithms
- Travelling Salesman Problem
- 2 – 3 Trees Algorithm
- Kruskal's (P) and Prim's (K) Algorithms
- Algorithm for fractional knapsack problem
- Algorithm and procedure to solve a longest common subsequence problem
- Midpoint Circle Algorithm
- Multistage graph problem with forward approach and backward approach algorithms
- Floyd Warshall algorithm with its Pseudo Code
- Reliability design problem
- Removing consecutive duplicates from a string
- Fast Exponentiation using Bitmasking

Comments and Discussions!