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Greatest Common Divisor (GCD) of 198 and 158

The greatest common divisor (GCD) of 198 and 158 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 158?

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 ÷ 158 = 1 remainder 40
2 158 ÷ 40 = 3 remainder 38
3 40 ÷ 38 = 1 remainder 2
4 38 ÷ 2 = 19 remainder 0

Examples of GCD Calculations

NumbersGCD
93 and 1761
24 and 1911
81 and 513
175 and 261
123 and 423

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