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Greatest Common Divisor (GCD) of 119 and 67

The greatest common divisor (GCD) of 119 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 119 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
1 119 ÷ 67 = 1 remainder 52
2 67 ÷ 52 = 1 remainder 15
3 52 ÷ 15 = 3 remainder 7
4 15 ÷ 7 = 2 remainder 1
5 7 ÷ 1 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
143 and 821
188 and 311
158 and 1351
155 and 1281
164 and 1222

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