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Greatest Common Divisor (GCD) of 174 and 124

The greatest common divisor (GCD) of 174 and 124 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 174 and 124?

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 ÷ 124 = 1 remainder 50
2 124 ÷ 50 = 2 remainder 24
3 50 ÷ 24 = 2 remainder 2
4 24 ÷ 2 = 12 remainder 0

Examples of GCD Calculations

NumbersGCD
75 and 1555
77 and 1061
56 and 382
50 and 17010
166 and 1682

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