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Greatest Common Divisor (GCD) of 106 and 119

The greatest common divisor (GCD) of 106 and 119 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 119?

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 ÷ 119 = 0 remainder 106
2 119 ÷ 106 = 1 remainder 13
3 106 ÷ 13 = 8 remainder 2
4 13 ÷ 2 = 6 remainder 1
5 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
165 and 5555
109 and 1591
123 and 921
10 and 1022
104 and 764

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