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Greatest Common Divisor (GCD) of 128 and 126

The greatest common divisor (GCD) of 128 and 126 is 2.

What is the Greatest Common Divisor (GCD)?

The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.

How to Calculate the GCD of 128 and 126?

We use the Euclidean algorithm, which involves the following steps:

  1. Divide the larger number by the smaller number.
  2. Replace the larger number with the smaller number and the smaller number with the remainder from the division.
  3. Repeat this process until the remainder is zero.
  4. The non-zero remainder just before zero is the GCD.

Step-by-Step Euclidean Algorithm

StepCalculation
1 128 ÷ 126 = 1 remainder 2
2 126 ÷ 2 = 63 remainder 0

Examples of GCD Calculations

NumbersGCD
191 and 511
63 and 1757
79 and 171
193 and 1171
154 and 1791

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