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Greatest Common Divisor (GCD) of 194 and 33

The greatest common divisor (GCD) of 194 and 33 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 194 and 33?

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
1 194 ÷ 33 = 5 remainder 29
2 33 ÷ 29 = 1 remainder 4
3 29 ÷ 4 = 7 remainder 1
4 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
82 and 1091
189 and 1661
89 and 781
162 and 606
30 and 342

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