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Greatest Common Divisor (GCD) of 191 and 50

The greatest common divisor (GCD) of 191 and 50 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 191 and 50?

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
1 191 ÷ 50 = 3 remainder 41
2 50 ÷ 41 = 1 remainder 9
3 41 ÷ 9 = 4 remainder 5
4 9 ÷ 5 = 1 remainder 4
5 5 ÷ 4 = 1 remainder 1
6 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
170 and 1031
129 and 303
83 and 581
180 and 1971
169 and 13013

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