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Greatest Common Divisor (GCD) of 179 and 66

The greatest common divisor (GCD) of 179 and 66 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 179 and 66?

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
1 179 ÷ 66 = 2 remainder 47
2 66 ÷ 47 = 1 remainder 19
3 47 ÷ 19 = 2 remainder 9
4 19 ÷ 9 = 2 remainder 1
5 9 ÷ 1 = 9 remainder 0

Examples of GCD Calculations

NumbersGCD
186 and 1011
33 and 761
149 and 111
43 and 781
192 and 9696

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