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Greatest Common Divisor (GCD) of 134 and 146

The greatest common divisor (GCD) of 134 and 146 is 2.

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 134 and 146?

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
1 134 ÷ 146 = 0 remainder 134
2 146 ÷ 134 = 1 remainder 12
3 134 ÷ 12 = 11 remainder 2
4 12 ÷ 2 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
121 and 461
109 and 1821
129 and 381
110 and 1131
170 and 1091

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