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Greatest Common Divisor (GCD) of 199 and 93

The greatest common divisor (GCD) of 199 and 93 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 199 and 93?

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
1 199 ÷ 93 = 2 remainder 13
2 93 ÷ 13 = 7 remainder 2
3 13 ÷ 2 = 6 remainder 1
4 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
137 and 1611
54 and 382
47 and 1761
184 and 771
147 and 1241

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