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Greatest Common Divisor (GCD) of 110 and 106

The greatest common divisor (GCD) of 110 and 106 is 2.

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 110 and 106?

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
1 110 ÷ 106 = 1 remainder 4
2 106 ÷ 4 = 26 remainder 2
3 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
125 and 421
44 and 1231
91 and 497
175 and 921
99 and 303

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