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Greatest Common Divisor (GCD) of 66 and 54

The greatest common divisor (GCD) of 66 and 54 is 6.

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 66 and 54?

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 66 ÷ 54 = 1 remainder 12
2 54 ÷ 12 = 4 remainder 6
3 12 ÷ 6 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
142 and 591
155 and 831
110 and 971
47 and 971
57 and 1893

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