HowManyNumbers Logo

Greatest Common Divisor (GCD) of 186 and 100

The greatest common divisor (GCD) of 186 and 100 is 2.

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 100?

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 ÷ 100 = 1 remainder 86
2 100 ÷ 86 = 1 remainder 14
3 86 ÷ 14 = 6 remainder 2
4 14 ÷ 2 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
136 and 1231
46 and 1451
189 and 189
76 and 1102
136 and 1851

Try Calculating GCD of Other Numbers







Related Calculators