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Greatest Common Divisor (GCD) of 107 and 27

The greatest common divisor (GCD) of 107 and 27 is 1.

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 107 and 27?

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
1 107 ÷ 27 = 3 remainder 26
2 27 ÷ 26 = 1 remainder 1
3 26 ÷ 1 = 26 remainder 0

Examples of GCD Calculations

NumbersGCD
135 and 1743
185 and 1421
188 and 1484
147 and 1241
142 and 1122

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