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Greatest Common Divisor (GCD) of 114 and 185

The greatest common divisor (GCD) of 114 and 185 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 114 and 185?

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
1 114 ÷ 185 = 0 remainder 114
2 185 ÷ 114 = 1 remainder 71
3 114 ÷ 71 = 1 remainder 43
4 71 ÷ 43 = 1 remainder 28
5 43 ÷ 28 = 1 remainder 15
6 28 ÷ 15 = 1 remainder 13
7 15 ÷ 13 = 1 remainder 2
8 13 ÷ 2 = 6 remainder 1
9 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
63 and 1931
116 and 351
69 and 303
90 and 711
142 and 962

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