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# Find GCD of two numbers

In mathematics, Greatest Common Divisor (GCD) is the largest possible integer, that divides both of the integers. The condition is that the numbers must be non-zero.

We will follow the Euclidean Algorithm to find the GCD of two numbers.

## Input and Output

Input: Two numbers 51 and 34 Output: The GCD is: 17

## Algorithm

findGCD(a, b)

**Input:** Two numbers a and b.

**Output:** GCD of a and b.

Begin if a = 0 OR b = 0, then return 0 if a = b, then return b if a > b, then return findGCD(a-b, b) else return findGCD(a, b-a) End

## Example

#include<iostream> using namespace std; int findGCD(int a, int b) { //assume a is greater than b if(a == 0 || b == 0) return 0; //as a and b are 0, the greatest divisior is also 0 if(a==b) return b; //when both numbers are same if(a>b) return findGCD(a-b, b); else return findGCD(a, b-a); } int main() { int a, b; cout << "Enter Two numbers to find GCD: "; cin >> a >> b; cout << "The GCD is: " << findGCD(a,b); }

## Output

Enter Two numbers to find GCD: 51 34 The GCD is: 17

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