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Greatest Common Divisor (GCD) of 186 and 90

The greatest common divisor (GCD) of 186 and 90 is 6.

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 186 and 90?

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
1 186 ÷ 90 = 2 remainder 6
2 90 ÷ 6 = 15 remainder 0

Examples of GCD Calculations

NumbersGCD
19 and 1981
103 and 451
173 and 1641
84 and 1671
162 and 1179

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