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Greatest Common Divisor (GCD) of 174 and 174

The greatest common divisor (GCD) of 174 and 174 is 174.

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 174 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
1 174 ÷ 174 = 1 remainder 0

Examples of GCD Calculations

NumbersGCD
151 and 1351
41 and 881
101 and 361
179 and 1441
115 and 1681

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