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Greatest Common Divisor (GCD) of 197 and 33

The greatest common divisor (GCD) of 197 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 197 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
1 197 ÷ 33 = 5 remainder 32
2 33 ÷ 32 = 1 remainder 1
3 32 ÷ 1 = 32 remainder 0

Examples of GCD Calculations

NumbersGCD
159 and 183
76 and 491
162 and 1102
66 and 1602
91 and 1651

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