Largest number that divides x and is co-prime with y

Given two positive numbers x and y. Find the maximum valued integer a such that:

1. a divides x i.e. x % a = 0
2. a and y are co-prime i.e. gcd(a, y) = 1

Examples :

Input : x = 15
y = 3
Output : a = 5
Explanation: 5 is the max integer
which satisfies both the conditions.
15 % 5 =0
gcd(5, 3) = 1
Hence, output is 5.

Input : x = 14
y = 28
Output : a = 1
Explanation: 14 % 1 =0
gcd(1, 28) = 1
Hence, output is 1.

Approach: Here, first we will remove the common factors of x and y from x by finding the greatest common divisor (gcd) of x and y and dividing x with that gcd.
Mathematically:

x = x / gcd(x, y) â€”â€” STEP1

Now, we repeat STEP1 till we get gcd(x, y) = 1.
At last, we return a = x

Algorithm:

Step 1: Define a function named gcd to find gcd of two numbers a and b.
Step 2: If a or b is equal to 0, return 0. If a is equal to b, return a.
Step 3: If a is greater than b, return gcd(a-b, b).
Step 4: If b is greater than a return gcd(a b-a).
Step 5: Define a function named cpFact to find the largest coprime divisor of two numbers x and y.
Step 6: While gcd(x, y) is not equal to 1, divide x by gcd(x,y).
Step 7: Return x as the largest coprime divisor.

below is the code implementation of the above approach:

C++

 // CPP program to find the // Largest Coprime Divisor   #include using namespace std;   // Recursive function to return gcd // of a and b int gcd(int a, int b) {     // Everything divides 0     if (a == 0 || b == 0)         return 0;       // base case     if (a == b)         return a;       // a is greater     if (a > b)         return gcd(a - b, b);     return gcd(a, b - a); }   // function to find largest // coprime divisor int cpFact(int x, int y) {     while (gcd(x, y) != 1) {         x = x / gcd(x, y);     }     return x; }   // divisor code int main() {     int x = 15;     int y = 3;     cout << cpFact(x, y) << endl;     x = 14;     y = 28;     cout << cpFact(x, y) << endl;     x = 7;     y = 3;     cout << cpFact(x, y);     return 0; }

Java

 // java program to find the // Largest Coprime Divisor import java.io.*;   class GFG {     // Recursive function to return gcd     // of a and b     static int gcd(int a, int b)     {         // Everything divides 0         if (a == 0 || b == 0)             return 0;           // base case         if (a == b)             return a;           // a is greater         if (a > b)             return gcd(a - b, b);         return gcd(a, b - a);     }       // function to find largest     // coprime divisor     static int cpFact(int x, int y)     {         while (gcd(x, y) != 1) {             x = x / gcd(x, y);         }         return x;     }       // divisor code     public static void main(String[] args)     {         int x = 15;         int y = 3;         System.out.println(cpFact(x, y));         x = 14;         y = 28;         System.out.println(cpFact(x, y));         x = 7;         y = 3;         System.out.println(cpFact(x, y));     } }   //

Python3

 # Python3 code to find the # Largest Coprime Divisor   # Recursive function to return # gcd of a and b def gcd (a, b):           # Everything divides 0     if a == 0 or b == 0:         return 0           # base case     if a == b:         return a               # a is greater     if a > b:         return gcd(a - b, b)           return gcd(a, b - a)   # function to find largest # coprime divisor def cpFact(x, y):     while gcd(x, y) != 1:         x = x / gcd(x, y)     return int(x)       # divisor code x = 15 y = 3 print(cpFact(x, y)) x = 14 y = 28 print(cpFact(x, y)) x = 7 y = 3 print(cpFact(x, y))   # This code is contributed by "Sharad_Bhardwaj".

C#

 // C# program to find the // Largest Coprime Divisor using System;   class GFG {       // Recursive function to return gcd     // of a and b     static int gcd(int a, int b)     {           // Everything divides 0         if (a == 0 || b == 0)             return 0;           // base case         if (a == b)             return a;           // a is greater         if (a > b)             return gcd(a - b, b);           return gcd(a, b - a);     }       // function to find largest     // coprime divisor     static int cpFact(int x, int y)     {         while (gcd(x, y) != 1) {             x = x / gcd(x, y);         }           return x;     }       // divisor code     public static void Main()     {           int x = 15;         int y = 3;         Console.WriteLine(cpFact(x, y));           x = 14;         y = 28;         Console.WriteLine(cpFact(x, y));           x = 7;         y = 3;         Console.WriteLine(cpFact(x, y));     } }   // This code is contributed by vt_m.

PHP

 \$b)         return gcd(\$a - \$b, \$b);     return gcd(\$a, \$b - \$a); }   // function to find largest // coprime divisor function cpFact( \$x, \$y) {     while (gcd(\$x, \$y) != 1)     {         \$x = \$x / gcd(\$x, \$y);     }     return \$x; }   // Driver Code \$x = 15; \$y = 3; echo cpFact(\$x, \$y), "\n"; \$x = 14; \$y = 28; echo cpFact(\$x, \$y), "\n"; \$x = 7; \$y = 3; echo cpFact(\$x, \$y);   // This code is contributed by aj_36 ?>

Javascript



Output :

5
1
7

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