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Greatest Common Divisor (GCD) of 164 and 18

The greatest common divisor (GCD) of 164 and 18 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 164 and 18?

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
1 164 ÷ 18 = 9 remainder 2
2 18 ÷ 2 = 9 remainder 0

Examples of GCD Calculations

NumbersGCD
79 and 1041
185 and 1941
104 and 151
69 and 1521
162 and 5454

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