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Understanding Euclid's Algorithm for GCD Calculation in Java

This Java program demonstrates the implementation of Euclid's algorithm to compute the greatest common divisor (GCD) of two integers. The algorithm uses recursion to efficiently find the GCD by repeatedly applying the modulo operation until one of the numbers becomes zero. The main method takes two integer inputs from the command line, calls the GCD function, and prints the result. This example highlights the simplicity and elegance of recursive functions in programming.

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Understanding Euclid's Algorithm for GCD Calculation in Java

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  1. Recursive GCD Demo publicclass Euclid { public staticint gcd(int p,int q) { if(q ==0)return p; elsereturn gcd(q, p % q); } publicstaticvoid main(String[] args) { int p = Integer.parseInt(args[0]); int q = Integer.parseInt(args[1]); System.out.println(gcd(p, q)); } }

  2. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) p = 1272, q = 216 environment

  3. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) p = 1272, q = 216 environment

  4. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) p = 1272, q = 216 environment

  5. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) p = 216, q = 192 p = 1272, q = 216 environment environment 1272 = 216  5 + 192

  6. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) p = 1272, q = 216 p = 216, q = 192 environment environment

  7. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) p = 1272, q = 216 p = 216, q = 192 environment environment

  8. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) p = 216, q = 192 p = 1272, q = 216 environment environment p = 192, q = 24 environment

  9. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) p = 216, q = 192 p = 1272, q = 216 environment environment p = 192, q = 24 environment

  10. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) p = 216, q = 192 p = 1272, q = 216 environment environment p = 192, q = 24 environment

  11. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(24, 0) p = 216, q = 192 p = 1272, q = 216 environment environment p = 192, q = 24 environment p = 24, q = 0 environment

  12. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(24, 0) p = 216, q = 192 p = 1272, q = 216 environment environment p = 192, q = 24 environment p = 24, q = 0 environment

  13. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(24, 0) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) gcd(216, 192) p = 1272, q = 216 p = 216, q = 192 environment environment p = 192, q = 24 environment p = 24, q = 0 24 environment

  14. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) p = 216, q = 192 p = 1272, q = 216 environment environment p = 192, q = 24 environment 24

  15. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(192, 24) p = 216, q = 192 p = 1272, q = 216 environment environment 24 p = 192, q = 24 environment 24

  16. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) p = 216, q = 192 p = 1272, q = 216 environment environment 24

  17. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(216, 192) p = 216, q = 192 p = 1272, q = 216 environment environment 24 24

  18. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) p = 1272, q = 216 environment 24

  19. static int gcd(int p, int q){ if (q ==0) return p; else return gcd(q, p % q); } gcd(1272, 216) p = 1272, q = 216 environment 24 publicclass Euclid { public staticint gcd(int p,int q) { if(q ==0)return p; elsereturn gcd(q, p % q); } publicstaticvoid main(String[] args) { int p = Integer.parseInt(args[0]); int q = Integer.parseInt(args[1]); System.out.println(gcd(p, q)); } } 24 24 % java Euclid 1272 216 24

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