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Greatest Common Divisor (GCD) of 123 and 119

The greatest common divisor (GCD) of 123 and 119 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 123 and 119?

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
1 123 ÷ 119 = 1 remainder 4
2 119 ÷ 4 = 29 remainder 3
3 4 ÷ 3 = 1 remainder 1
4 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
24 and 531
124 and 351
115 and 741
144 and 1848
26 and 442

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