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Greatest Common Divisor (GCD) of 60 and 186

The greatest common divisor (GCD) of 60 and 186 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 60 and 186?

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 60 ÷ 186 = 0 remainder 60
2 186 ÷ 60 = 3 remainder 6
3 60 ÷ 6 = 10 remainder 0

Examples of GCD Calculations

NumbersGCD
131 and 501
62 and 971
16 and 1291
60 and 1484
165 and 321

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