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Greatest Common Divisor (GCD) of 105 and 191

The greatest common divisor (GCD) of 105 and 191 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 105 and 191?

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
1 105 ÷ 191 = 0 remainder 105
2 191 ÷ 105 = 1 remainder 86
3 105 ÷ 86 = 1 remainder 19
4 86 ÷ 19 = 4 remainder 10
5 19 ÷ 10 = 1 remainder 9
6 10 ÷ 9 = 1 remainder 1
7 9 ÷ 1 = 9 remainder 0

Examples of GCD Calculations

NumbersGCD
27 and 1241
72 and 1473
59 and 1171
55 and 871
135 and 881

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