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Greatest Common Divisor (GCD) of 129 and 89

The greatest common divisor (GCD) of 129 and 89 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 89?

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 ÷ 89 = 1 remainder 40
2 89 ÷ 40 = 2 remainder 9
3 40 ÷ 9 = 4 remainder 4
4 9 ÷ 4 = 2 remainder 1
5 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
68 and 1782
50 and 431
165 and 981
78 and 1882
56 and 1804

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