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Greatest Common Divisor (GCD) of 119 and 31

The greatest common divisor (GCD) of 119 and 31 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 31?

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 ÷ 31 = 3 remainder 26
2 31 ÷ 26 = 1 remainder 5
3 26 ÷ 5 = 5 remainder 1
4 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
61 and 1681
80 and 371
80 and 531
180 and 1179
94 and 1822

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