Java How To Find the GCD

Find the Greatest Common Divisor (GCD)

The GCD (Greatest Common Divisor) is the largest number that divides two numbers without leaving a remainder.

int a = 36;
int b = 60;
int gcd = 1;

for (int i = 1; i <= a && i <= b; i++) {
  if (a % i == 0 && b % i == 0) {
    gcd = i;
  }
}

System.out.println("GCD: " + gcd);

Explanation:

We want the largest number that divides both 36 and 60 without a remainder.

• The loop starts at 1 and goes up to the smaller number (36).
• At each step, we check if i divides both numbers (using %, the remainder operator).
• If it does, we update gcd to that value.

For example:

• 36 % 12 == 0 and 60 % 12 == 0, so 12 is a divisor of both.
• Later, the loop finds gcd = 12 as the largest common divisor.

So the program prints GCD: 12.