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Greatest Common Divisor (GCD) of 29 and 184

The greatest common divisor (GCD) of 29 and 184 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 29 and 184?

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 29 ÷ 184 = 0 remainder 29
2 184 ÷ 29 = 6 remainder 10
3 29 ÷ 10 = 2 remainder 9
4 10 ÷ 9 = 1 remainder 1
5 9 ÷ 1 = 9 remainder 0

Examples of GCD Calculations

NumbersGCD
105 and 111
84 and 333
181 and 2001
164 and 791
167 and 401

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