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Greatest Common Divisor (GCD) of 130 and 128

The greatest common divisor (GCD) of 130 and 128 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 130 and 128?

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
1 130 ÷ 128 = 1 remainder 2
2 128 ÷ 2 = 64 remainder 0

Examples of GCD Calculations

NumbersGCD
130 and 1862
47 and 881
158 and 682
139 and 1041
124 and 924

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