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Greatest Common Divisor (GCD) of 108 and 74

The greatest common divisor (GCD) of 108 and 74 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 108 and 74?

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
1 108 ÷ 74 = 1 remainder 34
2 74 ÷ 34 = 2 remainder 6
3 34 ÷ 6 = 5 remainder 4
4 6 ÷ 4 = 1 remainder 2
5 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
48 and 1751
118 and 302
132 and 10812
166 and 571
119 and 1311

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