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Greatest Common Divisor (GCD) of 66 and 168

The greatest common divisor (GCD) of 66 and 168 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 168?

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 ÷ 168 = 0 remainder 66
2 168 ÷ 66 = 2 remainder 36
3 66 ÷ 36 = 1 remainder 30
4 36 ÷ 30 = 1 remainder 6
5 30 ÷ 6 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
70 and 1211
88 and 1311
144 and 1611
28 and 1804
114 and 1222

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