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Greatest Common Divisor (GCD) of 181 and 114

The greatest common divisor (GCD) of 181 and 114 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 181 and 114?

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
1 181 ÷ 114 = 1 remainder 67
2 114 ÷ 67 = 1 remainder 47
3 67 ÷ 47 = 1 remainder 20
4 47 ÷ 20 = 2 remainder 7
5 20 ÷ 7 = 2 remainder 6
6 7 ÷ 6 = 1 remainder 1
7 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
26 and 1902
153 and 1301
94 and 1422
112 and 917
107 and 1631

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