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Greatest Common Divisor (GCD) of 131 and 67

The greatest common divisor (GCD) of 131 and 67 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 131 and 67?

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
1 131 ÷ 67 = 1 remainder 64
2 67 ÷ 64 = 1 remainder 3
3 64 ÷ 3 = 21 remainder 1
4 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
105 and 171
82 and 1742
112 and 8016
139 and 1081
169 and 661

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