# Program to find GCD or HCF of two numbers using Middle School Procedure

Given two positive integers M and N, the task is to find the greatest common divisor (GCD) using Middle School Procedure.
Note: GCD of two integers is the largest positive integer that divides both of the integers.

Examples:

```Input: m = 12, n = 14
Output: 2
Prime factor of 12 =  1*2*2*3
Prime factor of 14 = 1*2*7
GCD(12, 14) = 2

Input: m = 5, n = 10
Output: 5
Prime factor of 10 = 1*2*5
Prime factor of 5 = 1*5
GCD(5, 10) = 5
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The algorithm to find GCD using Middle School procedure GCD(m, n):

1. Find the prime factorization of m.
2. Find the prime factorization of n.
3. Find all the common prime factors.
4. Compute the product of all the common prime factors and return it as gcd(m, n).

Below is the implementation of above algorithm:

## C++

 `// C++ implementation of above algorithm ` `#include ` `#define MAXFACTORS 1024 ` `using` `namespace` `std; ` ` `  `// struct to store factorization of m and n ` `typedef` `struct` `{ ` ` `  `    ``int` `size; ` `    ``int` `factor[MAXFACTORS + 1]; ` `    ``int` `exponent[MAXFACTORS + 1]; ` ` `  `} FACTORIZATION; ` ` `  `// Function to find the factorization of M and N ` `void` `FindFactorization(``int` `x, FACTORIZATION* factorization) ` `{ ` `    ``int` `i, j = 1; ` `    ``int` `n = x, c = 0; ` `    ``int` `k = 1; ` `    ``factorization->factor = 1; ` `    ``factorization->exponent = 1; ` ` `  `    ``for` `(i = 2; i <= n; i++) { ` `        ``c = 0; ` ` `  `        ``while` `(n % i == 0) { ` `            ``c++; ` ` `  `            ``// factorization->factor[j]=i; ` `            ``n = n / i; ` `            ``// j++; ` `        ``} ` ` `  `        ``if` `(c > 0) { ` `            ``factorization->exponent[k] = c; ` `            ``factorization->factor[k] = i; ` `            ``k++; ` `        ``} ` `    ``} ` ` `  `    ``factorization->size = k - 1; ` `} ` ` `  `// Function to print the factors ` `void` `DisplayFactorization(``int` `x, FACTORIZATION factorization) ` `{ ` ` `  `    ``int` `i; ` `    ``cout << ``"Prime factor of << x << = "``; ` ` `  `    ``for` `(i = 0; i <= factorization.size; i++) { ` ` `  `        ``cout << factorization.factor[i]; ` ` `  `        ``if` `(factorization.exponent[i] > 1) ` `            ``cout << ``"^"` `<< factorization.exponent[i]; ` ` `  `        ``if` `(i < factorization.size) ` `            ``cout << ``"*"``; ` ` `  `        ``else` `            ``cout << ``"\n"``; ` `    ``} ` `} ` ` `  `// function to find the gcd using Middle School procedure ` `int` `gcdMiddleSchoolProcedure(``int` `m, ``int` `n) ` `{ ` ` `  `    ``FACTORIZATION mFactorization, nFactorization; ` ` `  `    ``int` `r, mi, ni, i, k, x = 1, j; ` ` `  `    ``// Step 1. ` `    ``FindFactorization(m, &mFactorization); ` `    ``DisplayFactorization(m, mFactorization); ` ` `  `    ``// Step 2. ` `    ``FindFactorization(n, &nFactorization); ` `    ``DisplayFactorization(n, nFactorization); ` ` `  `    ``// Steps 3 and 4. ` `    ``// Procedure algorithm for computing the ` `    ``// greatest common divisor. ` `    ``int` `min; ` `    ``i = 1; ` `    ``j = 1; ` `    ``while` `(i <= mFactorization.size && j <= nFactorization.size) { ` `        ``if` `(mFactorization.factor[i] < nFactorization.factor[j]) ` `            ``i++; ` ` `  `        ``else` `if` `(nFactorization.factor[j] < mFactorization.factor[i]) ` `            ``j++; ` ` `  `        ``else` `/* if arr1[i] == arr2[j] */` `        ``{ ` `            ``min = mFactorization.exponent[i] > nFactorization.exponent[j] ` `                      ``? nFactorization.exponent[j] ` `                      ``: mFactorization.exponent[i]; ` ` `  `            ``x = x * mFactorization.factor[i] * min; ` `            ``i++; ` `            ``j++; ` `        ``} ` `    ``} ` ` `  `    ``return` `x; ` `} ` ` `  `// Driver code ` `int` `main() ` ` `  `{ ` ` `  `    ``int` `m = 10, n = 15; ` `    ``cout << ``"GCD("` `<< m << ``", "` `<< n << ``") = "` `         ``<< gcdMiddleSchoolProcedure(m, n); ` ` `  `    ``return` `(0); ` `} `

## Java

 `// Java implementation of above algorithm  ` `class` `GFG ` `{ ` `static` `final` `int` `MAXFACTORS = ``1024` `; ` ` `  `// class to store factorization  ` `// of m and n  ` `static` `class` `FACTORIZATION ` `{  ` `    ``int` `size;  ` `    ``int` `factor[] = ``new` `int``[MAXFACTORS + ``1``];  ` `    ``int` `exponent[] = ``new` `int``[MAXFACTORS + ``1``];  ` ` `  `}  ` ` `  `// Function to find the  ` `// factorization of M and N  ` `static` `void` `FindFactorization(``int` `x, FACTORIZATION  ` `                                     ``factorization)  ` `{  ` `    ``int` `i, j = ``1``;  ` `    ``int` `n = x, c = ``0``;  ` `    ``int` `k = ``1``;  ` `    ``factorization.factor[``0``] = ``1``;  ` `    ``factorization.exponent[``0``] = ``1``;  ` ` `  `    ``for` `(i = ``2``; i <= n; i++)  ` `    ``{  ` `        ``c = ``0``;  ` ` `  `        ``while` `(n % i == ``0``)  ` `        ``{  ` `            ``c++;  ` ` `  `            ``// factorization.factor[j]=i;  ` `            ``n = n / i;  ` `            ``// j++;  ` `        ``}  ` ` `  `        ``if` `(c > ``0``)  ` `        ``{  ` `            ``factorization.exponent[k] = c;  ` `            ``factorization.factor[k] = i;  ` `            ``k++;  ` `        ``}  ` `    ``}  ` ` `  `    ``factorization.size = k - ``1``;  ` `}  ` ` `  `// Function to print the factors  ` `static` `void` `DisplayFactorization(``int` `x, FACTORIZATION  ` `                                        ``factorization)  ` `{  ` `    ``int` `i;  ` `    ``System.out.print(``"Prime factor of "` `+ x + ``" = "``);  ` ` `  `    ``for` `(i = ``0``; ` `         ``i <= factorization.size; i++) ` `    ``{  ` ` `  `        ``System.out.print(factorization.factor[i]);  ` ` `  `        ``if` `(factorization.exponent[i] > ``1``)  ` `            ``System.out.print( ``"^"` `+ ` `                       ``factorization.exponent[i]);  ` ` `  `        ``if` `(i < factorization.size)  ` `            ``System.out.print(``"*"``);  ` ` `  `        ``else` `            ``System.out.println( );  ` `    ``}  ` `}  ` ` `  `// function to find the gcd  ` `// using Middle School procedure  ` `static` `int` `gcdMiddleSchoolProcedure(``int` `m, ``int` `n)  ` `{  ` ` `  `    ``FACTORIZATION mFactorization = ``new` `FACTORIZATION(); ` `    ``FACTORIZATION nFactorization = ``new` `FACTORIZATION();  ` ` `  `    ``int` `r, mi, ni, i, k, x = ``1``, j;  ` ` `  `    ``// Step 1.  ` `    ``FindFactorization(m, mFactorization);  ` `    ``DisplayFactorization(m, mFactorization);  ` ` `  `    ``// Step 2.  ` `    ``FindFactorization(n, nFactorization);  ` `    ``DisplayFactorization(n, nFactorization);  ` ` `  `    ``// Steps 3 and 4.  ` `    ``// Procedure algorithm for computing the  ` `    ``// greatest common divisor.  ` `    ``int` `min;  ` `    ``i = ``1``;  ` `    ``j = ``1``;  ` `    ``while` `(i <= mFactorization.size &&  ` `           ``j <= nFactorization.size)  ` `    ``{  ` `        ``if` `(mFactorization.factor[i] <  ` `            ``nFactorization.factor[j])  ` `            ``i++;  ` ` `  `        ``else` `if` `(nFactorization.factor[j] <  ` `                 ``mFactorization.factor[i])  ` `            ``j++;  ` ` `  `        ``else` `/* if arr1[i] == arr2[j] */` `        ``{  ` `            ``min = mFactorization.exponent[i] >  ` `                  ``nFactorization.exponent[j] ? ` `                  ``nFactorization.exponent[j] : ` `                  ``mFactorization.exponent[i];  ` ` `  `            ``x = x * mFactorization.factor[i] * min;  ` `            ``i++;  ` `            ``j++;  ` `        ``}  ` `    ``}  ` ` `  `    ``return` `x;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String args[]) ` `{  ` `    ``int` `m = ``10``, n = ``15``;  ` `    ``System.out.print(``"GCD("` `+ m + ``", "` `+ n + ``") = "` `+  ` `                     ``gcdMiddleSchoolProcedure(m, n));  ` `}  ` `} ` ` `  `// This code is contributed by Arnab Kundu `

## C#

 `// C# implementation of above algorithm  ` `using` `System; ` `     `  `public` `class` `GFG ` `{ ` `static` `readonly` `int` `MAXFACTORS = 1024 ; ` ` `  `// class to store factorization  ` `// of m and n  ` `public` `class` `FACTORIZATION ` `{  ` `    ``public` `int` `size;  ` `    ``public` `int` `[]factor = ``new` `int``[MAXFACTORS + 1];  ` `    ``public` `int` `[]exponent = ``new` `int``[MAXFACTORS + 1];  ` ` `  `}  ` ` `  `// Function to find the  ` `// factorization of M and N  ` `static` `void` `FindFactorization(``int` `x, FACTORIZATION  ` `                                    ``factorization)  ` `{  ` `    ``int` `i;  ` `    ``int` `n = x, c = 0;  ` `    ``int` `k = 1;  ` `    ``factorization.factor = 1;  ` `    ``factorization.exponent = 1;  ` ` `  `    ``for` `(i = 2; i <= n; i++)  ` `    ``{  ` `        ``c = 0;  ` ` `  `        ``while` `(n % i == 0)  ` `        ``{  ` `            ``c++;  ` ` `  `            ``// factorization.factor[j]=i;  ` `            ``n = n / i;  ` `            ``// j++;  ` `        ``}  ` ` `  `        ``if` `(c > 0)  ` `        ``{  ` `            ``factorization.exponent[k] = c;  ` `            ``factorization.factor[k] = i;  ` `            ``k++;  ` `        ``}  ` `    ``}  ` ` `  `    ``factorization.size = k - 1;  ` `}  ` ` `  `// Function to print the factors  ` `static` `void` `DisplayFactorization(``int` `x, FACTORIZATION  ` `                                        ``factorization)  ` `{  ` `    ``int` `i;  ` `    ``Console.Write(``"Prime factor of "` `+ x + ``" = "``);  ` ` `  `    ``for` `(i = 0; ` `        ``i <= factorization.size; i++) ` `    ``{  ` ` `  `        ``Console.Write(factorization.factor[i]);  ` ` `  `        ``if` `(factorization.exponent[i] > 1)  ` `            ``Console.Write( ``"^"` `+ ` `                    ``factorization.exponent[i]);  ` ` `  `        ``if` `(i < factorization.size)  ` `            ``Console.Write(``"*"``);  ` ` `  `        ``else` `        ``Console.WriteLine();  ` `    ``}  ` `}  ` ` `  `// function to find the gcd  ` `// using Middle School procedure  ` `static` `int` `gcdMiddleSchoolProcedure(``int` `m, ``int` `n)  ` `{  ` ` `  `    ``FACTORIZATION mFactorization = ``new` `FACTORIZATION(); ` `    ``FACTORIZATION nFactorization = ``new` `FACTORIZATION();  ` ` `  `    ``int` `i, x = 1, j;  ` ` `  `    ``// Step 1.  ` `    ``FindFactorization(m, mFactorization);  ` `    ``DisplayFactorization(m, mFactorization);  ` ` `  `    ``// Step 2.  ` `    ``FindFactorization(n, nFactorization);  ` `    ``DisplayFactorization(n, nFactorization);  ` ` `  `    ``// Steps 3 and 4.  ` `    ``// Procedure algorithm for computing the  ` `    ``// greatest common divisor.  ` `    ``int` `min;  ` `    ``i = 1;  ` `    ``j = 1;  ` `    ``while` `(i <= mFactorization.size &&  ` `        ``j <= nFactorization.size)  ` `    ``{  ` `        ``if` `(mFactorization.factor[i] <  ` `            ``nFactorization.factor[j])  ` `            ``i++;  ` ` `  `        ``else` `if` `(nFactorization.factor[j] <  ` `                ``mFactorization.factor[i])  ` `            ``j++;  ` ` `  `        ``else` `/* if arr1[i] == arr2[j] */` `        ``{  ` `            ``min = mFactorization.exponent[i] >  ` `                ``nFactorization.exponent[j] ? ` `                ``nFactorization.exponent[j] : ` `                ``mFactorization.exponent[i];  ` ` `  `            ``x = x * mFactorization.factor[i] * min;  ` `            ``i++;  ` `            ``j++;  ` `        ``}  ` `    ``}  ` ` `  `    ``return` `x;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main(String []args) ` `{  ` `    ``int` `m = 10, n = 15;  ` `    ``Console.Write(``"GCD("` `+ m + ``", "` `+ n + ``") = "` `+  ` `                    ``gcdMiddleSchoolProcedure(m, n));  ` `}  ` `} ` ` `  `// This code contribut by Rajput-Ji `

Output:

```Prime factor of 10 = 1*2*5
Prime factor of 15 = 1*3*5
GCD(10, 15) = 5
```

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Improved By : andrew1234, Rajput-Ji