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Greatest Common Divisor (GCD) of 114 and 178

The greatest common divisor (GCD) of 114 and 178 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 114 and 178?

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
1 114 ÷ 178 = 0 remainder 114
2 178 ÷ 114 = 1 remainder 64
3 114 ÷ 64 = 1 remainder 50
4 64 ÷ 50 = 1 remainder 14
5 50 ÷ 14 = 3 remainder 8
6 14 ÷ 8 = 1 remainder 6
7 8 ÷ 6 = 1 remainder 2
8 6 ÷ 2 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
196 and 244
10 and 5010
142 and 1282
146 and 542
64 and 471

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