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Greatest Common Divisor (GCD) of 106 and 187

The greatest common divisor (GCD) of 106 and 187 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 106 and 187?

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
1 106 ÷ 187 = 0 remainder 106
2 187 ÷ 106 = 1 remainder 81
3 106 ÷ 81 = 1 remainder 25
4 81 ÷ 25 = 3 remainder 6
5 25 ÷ 6 = 4 remainder 1
6 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
54 and 1451
108 and 1284
16 and 931
42 and 1522
85 and 1991

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