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Greatest Common Divisor (GCD) of 134 and 149

The greatest common divisor (GCD) of 134 and 149 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 134 and 149?

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 ÷ 149 = 0 remainder 134
2 149 ÷ 134 = 1 remainder 15
3 134 ÷ 15 = 8 remainder 14
4 15 ÷ 14 = 1 remainder 1
5 14 ÷ 1 = 14 remainder 0

Examples of GCD Calculations

NumbersGCD
126 and 1662
132 and 1284
45 and 231
179 and 1121
151 and 1661

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