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Greatest Common Divisor (GCD) of 129 and 26

The greatest common divisor (GCD) of 129 and 26 is 1.

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 129 and 26?

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
1 129 ÷ 26 = 4 remainder 25
2 26 ÷ 25 = 1 remainder 1
3 25 ÷ 1 = 25 remainder 0

Examples of GCD Calculations

NumbersGCD
112 and 782
29 and 1751
159 and 821
24 and 1062
131 and 1681

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