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Greatest Common Divisor (GCD) of 41 and 123

The greatest common divisor (GCD) of 41 and 123 is 41.

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 41 and 123?

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 41 ÷ 123 = 0 remainder 41
2 123 ÷ 41 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
184 and 862
104 and 1942
52 and 1591
10 and 1862
147 and 791

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