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Greatest Common Divisor (GCD) of 179 and 124

The greatest common divisor (GCD) of 179 and 124 is 1.

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 179 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
1 179 ÷ 124 = 1 remainder 55
2 124 ÷ 55 = 2 remainder 14
3 55 ÷ 14 = 3 remainder 13
4 14 ÷ 13 = 1 remainder 1
5 13 ÷ 1 = 13 remainder 0

Examples of GCD Calculations

NumbersGCD
106 and 1911
11 and 371
106 and 351
37 and 881
15 and 663

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