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Greatest Common Divisor (GCD) of 116 and 129

The greatest common divisor (GCD) of 116 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 116 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
1 116 ÷ 129 = 0 remainder 116
2 129 ÷ 116 = 1 remainder 13
3 116 ÷ 13 = 8 remainder 12
4 13 ÷ 12 = 1 remainder 1
5 12 ÷ 1 = 12 remainder 0

Examples of GCD Calculations

NumbersGCD
116 and 211
40 and 711
195 and 9113
175 and 1141
134 and 1451

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