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Greatest Common Divisor (GCD) of 129 and 55

The greatest common divisor (GCD) of 129 and 55 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 55?

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 ÷ 55 = 2 remainder 19
2 55 ÷ 19 = 2 remainder 17
3 19 ÷ 17 = 1 remainder 2
4 17 ÷ 2 = 8 remainder 1
5 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
69 and 1341
193 and 1811
76 and 342
195 and 1881
71 and 491

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