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Greatest Common Divisor (GCD) of 189 and 57

The greatest common divisor (GCD) of 189 and 57 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 189 and 57?

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
1 189 ÷ 57 = 3 remainder 18
2 57 ÷ 18 = 3 remainder 3
3 18 ÷ 3 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
31 and 101
19 and 651
139 and 271
138 and 2002
72 and 622

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