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Greatest Common Divisor (GCD) of 198 and 122

The greatest common divisor (GCD) of 198 and 122 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 198 and 122?

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
1 198 ÷ 122 = 1 remainder 76
2 122 ÷ 76 = 1 remainder 46
3 76 ÷ 46 = 1 remainder 30
4 46 ÷ 30 = 1 remainder 16
5 30 ÷ 16 = 1 remainder 14
6 16 ÷ 14 = 1 remainder 2
7 14 ÷ 2 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
116 and 822
157 and 331
191 and 191
180 and 1822
175 and 10025

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