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Greatest Common Divisor (GCD) of 106 and 129

The greatest common divisor (GCD) of 106 and 129 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 106 and 129?

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
1 106 ÷ 129 = 0 remainder 106
2 129 ÷ 106 = 1 remainder 23
3 106 ÷ 23 = 4 remainder 14
4 23 ÷ 14 = 1 remainder 9
5 14 ÷ 9 = 1 remainder 5
6 9 ÷ 5 = 1 remainder 4
7 5 ÷ 4 = 1 remainder 1
8 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
87 and 1821
195 and 1233
164 and 564
195 and 1313
192 and 1404

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