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Greatest Common Divisor (GCD) of 167 and 66

The greatest common divisor (GCD) of 167 and 66 is 1.

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 167 and 66?

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
1 167 ÷ 66 = 2 remainder 35
2 66 ÷ 35 = 1 remainder 31
3 35 ÷ 31 = 1 remainder 4
4 31 ÷ 4 = 7 remainder 3
5 4 ÷ 3 = 1 remainder 1
6 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
26 and 362
124 and 1724
66 and 1111
120 and 1611
175 and 221

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