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Greatest Common Divisor (GCD) of 84 and 14

The greatest common divisor (GCD) of 84 and 14 is 14.

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 84 and 14?

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 84 ÷ 14 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
93 and 1481
61 and 1741
180 and 1124
108 and 153
195 and 11739

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