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Greatest Common Divisor (GCD) of 138 and 171

The greatest common divisor (GCD) of 138 and 171 is 3.

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 138 and 171?

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
1 138 ÷ 171 = 0 remainder 138
2 171 ÷ 138 = 1 remainder 33
3 138 ÷ 33 = 4 remainder 6
4 33 ÷ 6 = 5 remainder 3
5 6 ÷ 3 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
63 and 521
16 and 1011
184 and 131
34 and 611
186 and 1002

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