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Greatest Common Divisor (GCD) of 106 and 165

The greatest common divisor (GCD) of 106 and 165 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 165?

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 ÷ 165 = 0 remainder 106
2 165 ÷ 106 = 1 remainder 59
3 106 ÷ 59 = 1 remainder 47
4 59 ÷ 47 = 1 remainder 12
5 47 ÷ 12 = 3 remainder 11
6 12 ÷ 11 = 1 remainder 1
7 11 ÷ 1 = 11 remainder 0

Examples of GCD Calculations

NumbersGCD
182 and 1782
144 and 306
64 and 542
161 and 1011
166 and 1671

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