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Greatest Common Divisor (GCD) of 104 and 55

The greatest common divisor (GCD) of 104 and 55 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 104 and 55?

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
1 104 ÷ 55 = 1 remainder 49
2 55 ÷ 49 = 1 remainder 6
3 49 ÷ 6 = 8 remainder 1
4 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
81 and 1241
144 and 1782
174 and 951
164 and 1071
166 and 622

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