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Greatest Common Divisor (GCD) of 192 and 183

The greatest common divisor (GCD) of 192 and 183 is 3.

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 192 and 183?

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
1 192 ÷ 183 = 1 remainder 9
2 183 ÷ 9 = 20 remainder 3
3 9 ÷ 3 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
99 and 1563
140 and 1182
25 and 761
95 and 1081
106 and 891

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