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Greatest Common Divisor (GCD) of 110 and 199

The greatest common divisor (GCD) of 110 and 199 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 110 and 199?

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
1 110 ÷ 199 = 0 remainder 110
2 199 ÷ 110 = 1 remainder 89
3 110 ÷ 89 = 1 remainder 21
4 89 ÷ 21 = 4 remainder 5
5 21 ÷ 5 = 4 remainder 1
6 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
24 and 786
21 and 1701
167 and 241
81 and 1563
128 and 1368

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