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Greatest Common Divisor (GCD) of 66 and 126

The greatest common divisor (GCD) of 66 and 126 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 126?

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 ÷ 126 = 0 remainder 66
2 126 ÷ 66 = 1 remainder 60
3 66 ÷ 60 = 1 remainder 6
4 60 ÷ 6 = 10 remainder 0

Examples of GCD Calculations

NumbersGCD
103 and 1141
160 and 1991
137 and 1191
33 and 1181
93 and 1323

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