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Greatest Common Divisor (GCD) of 94 and 174

The greatest common divisor (GCD) of 94 and 174 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 94 and 174?

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 94 ÷ 174 = 0 remainder 94
2 174 ÷ 94 = 1 remainder 80
3 94 ÷ 80 = 1 remainder 14
4 80 ÷ 14 = 5 remainder 10
5 14 ÷ 10 = 1 remainder 4
6 10 ÷ 4 = 2 remainder 2
7 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
109 and 109109
146 and 1391
22 and 682
30 and 213
187 and 3417

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